Implicit differentiation helps us find dy/dx even for relationships like that. This is done using the chain rule, and viewing y as an implicit function of x. For example, according to the chain …1. See formulas. Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=y. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation ... Gottfried Wilhelm von Leibniz (1646–1716), German philosopher, mathematician, and namesake of this widely used mathematical notation in calculus. In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small (or ... Nov 23, 2023 · Dy dx is the derivative of y with respect to x, while dx dy is the derivative of x with respect to y. The two operations have different properties and can be used for different purposes. For example, dy dx is often used to calculate the slope of a graph, while dx dy is more commonly used to calculate changes in the magnitude of a function over ... 18 Jan 2011 ... Tutorial on differentiation and finding dy/dx from dx/dy. YOUTUBE CHANNEL at https://www.youtube.com/ExamSolutions EXAMSOLUTIONS WEBSITE at ... dy/dx is differentiating an equation y with respect to x. d/dx is differentiating something that isn't necessarily an equation denoted by y. So for example if you have y=x 2 then dy/dx is the derivative of that, and is equivalent to d/dx (x 2) And the answer to both of them is 2x. [deleted] Differential equations of the form \frac {dy} {dx}=f (x) dxdy = f (x) are very common and easy to solve. The following shows how to do it: Step 1. First we multiply both sides by dx dx to obtain. dy=f (x)~dx. dy = f (x) dx. Step 2. Then we take the integral of both sides to obtain. \begin {aligned} \int dy&=\int f (x)~dx\\ y+C'&=\int f (x)~dx ... It is an overcast mid-November morning, and the sun keeps trying to break through the clouds, coming in and out like waves of the ocean. Edit Your Post Published by Genny Jessee on...To my knowledge, dy/dx is equal to the limit of (f(x+h) - f(x)) / h as h approaches zero. That is, dy is equal to the difference in the y value (f(x+h) - f(x)) and dx is equal to the difference in the x value (h) and dy/dx is equal to the rate of change of the y …What Is dYdX? dYdX is the developer of a leading non-custodial decentralized exchange (DEX) focused on advanced crypto products — namely derivatives like crypto perpertuals. dYdX runs on audited smart contracts on blockchains like Ethereum, which eliminates the need of trusted intermediaries.The origins of the name is obtained from the …it's separable!! y' = xy. 1 y y' = x. lny = x2 2 + C. y = ex2 2 +C. = αex2 2. Answer link. = alpha e^ {x^2/2 } it's separable!! y' = xy 1/y \ y' = x ln y = x^2/2 + C y = e^ {x^2/2 + C} = alpha e^ {x^2/2 }y = 3 x y = 3 x. Differentiate both sides of the equation. d dx (y) = d dx ( 3 x) d d x ( y) = d d x ( 3 x) The derivative of y y with respect to x x is y' y ′. y' y ′. Differentiate the right side of the equation. Tap for more steps... − 3 x2 - 3 x 2. Reform the equation by setting the left side equal to the right side.History and usage. The differential was first introduced via an intuitive or heuristic definition by Isaac Newton and furthered by Gottfried Leibniz, who thought of the differential dy as an infinitely small (or infinitesimal) change in the value y of the function, corresponding to an infinitely small change dx in the function's argument x.For that reason, the instantaneous …Chủ đề: dy/dx là gì Dy/Dx là một công cụ hữu ích trong toán học, giúp tính toán đạo hàm theo biến số x và y. Với công thức đạo hàm tổng quát, Dy/Dx cho phép các bạn tính độ dốc của đồ thị trong một khoảng xác định và từ đó suy ra các giá trị quan trọng khác. Không chỉ hỗ trợ trong việc giải toán đại ...A first order Differential Equation is Homogeneous when it can be in this form: dy dx = F ( y x ) We can solve it using Separation of Variables but first we create a new variable v = y x. v = y x which is also y = vx. And dy dx = d (vx) dx = v dx dx + x dv dx (by the Product Rule) Which can be simplified to dy dx = v + x dv dx.8 Feb 2021 ... Share your videos with friends, family, and the world.Find dy/dx y=2^x. Step 1. Differentiate both sides of the equation. Step 2. The derivative of with respect to is . Step 3. Differentiate using the Exponential Rule which states that is where =. Step 4. Reform the equation by setting the …11 Aug 2023 ... Ex 9.3, 6 For each of the differential equations in Exercises 1 to 10, find the general solution : dy/dx=(1+x^2 )(1+y^2 ) ...We can't know for sure exactly how we're going to die, but some ways of going are more common than others. The National Safety Council has calculated the probability of dying from ...Symbolab is the best derivative calculator, solving first derivatives, second derivatives, higher order derivatives, derivative at a point, partial derivatives, implicit derivatives, derivatives using definition, and more. Find dy/dx y=xsin(x) Step 1. Differentiate both sides of the equation. Step 2. The derivative of with respect to is . Step 3. Differentiate the right side of the ... 由于dy/dx定义的出发点，这个符号是一个整体，而不是一个可以拆开的东西。 微分形式、流形等等概念依然十分重要：之所以定义这些概念，是因为我们想在各种各样千奇百怪的几何上继续愉快地微积分；它们的定义也自然的包含了一元函数的情况——事实上 ...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchangeimplicit\:derivative\:\frac{dy}{dx},\:(x-y)^2=x+y-1 ; implicit\:derivative\:\frac{dy}{dx},\:x^3+y^3=4 ; … We write $\frac{dy}{dx}$ but this is just notational, convention really. First, it is important to remember that this is not a ratio (see this, which is an excellent discussion of $\frac{dy}{dx}$), it is a limit and there is a limit definition, see the brief section here for an idea. The idea is we approximate the change of functions using an ... Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly.laplace \frac{dy}{dx} en. Related Symbolab blog posts. Practice, practice, practice. Math can be an intimidating subject. Each new topic we learn has symbols and problems we have never seen. The unknowing... Enter a problem. Cooking Calculators.20 Dec 2015 ... Pakai cara apa ya dy/dx atau diturunin ? 1.y = (4x^4 - 6)^17 2.y = (sin x + cos x)^2 3.y = sin^5 √x^3 +2 msh binggung sma ini ,jawaban dr rumus ...dy/dx = 0. Slope = 0; y = linear function . y = ax + b. Straight line. dy/dx = a. Slope = coefficient on x. y = polynomial of order 2 or higher. y = ax n + b. Nonlinear, one or more turning points. dy/dx = anx n-1. Derivative is a function, actual slope depends upon location (i.e. value of x) y = sums or differences of 2 functions y = f(x) + g ...Given f ( x) = 10 x 5 + 7 x 2, find d y d x . Step 1: We will be using the power rule again because y is not a product or quotient of two functions. Step 2: Once again, since y = f ( x) we can ...Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.The derivative of a polar function r (θ) is dr/dθ. In this case, it is dr/dθ = -2sin (θ). If you plot r (θ) on the way that θ is on the horizontal axis and r is on the vertical axis, you get a simple cosine plot. But you can plot the r (θ) function on the (x,y) plane, in polar coordinates (r is the distance from origin and theta is the ...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeDifferentiation is used in maths for calculating rates of change. For example in mechanics, the rate of change of displacement (with respect to time) is the velocity. The rate of change of ...1) If y = x n, dy/dx = nx n-1. 2) If y = kx n, dy/dx = nkx n-1 (where k is a constant- in other words a number) Therefore to differentiate x to the power of something you bring the …16 Dec 2023 ... Topic: How to solve the differential equation dy/dx=1/x. Question: What is the solution of dy/dx=1/x? Answer: The general solution of ...By definition the derivative is the rate of change of y with regard to x. That's why RHS stands. As you realise dy dx d y x is not just a notation but it's mathematically how derivative is been defined. Since ) ′ () y x → 0 x → 0, the equation y …We’ve covered methods and rules to differentiate functions of the form y=f (x), where y is explicitly defined as... Save to Notebook! Free derivative calculator - differentiate functions with all the steps. Type in any function derivative to get the solution, steps and graph.18 Jan 2011 ... Tutorial on differentiation and finding dy/dx from dx/dy. YOUTUBE CHANNEL at https://www.youtube.com/ExamSolutions EXAMSOLUTIONS WEBSITE at ...y = 3 x y = 3 x. Differentiate both sides of the equation. d dx (y) = d dx ( 3 x) d d x ( y) = d d x ( 3 x) The derivative of y y with respect to x x is y' y ′. y' y ′. Differentiate the right side of the equation. Tap for more steps... − 3 x2 - 3 x 2. Reform the equation by setting the left side equal to the right side.So dy/dx literally means how the variable y changes as x changes. Imagine a graph, draw the line y = 1. It doesn't matter what value of x you look at, y = 1. It ... Implicit differentiation can help us solve inverse functions. The general pattern is: Start with the inverse equation in explicit form. Example: y = sin −1 (x) Rewrite it in non-inverse mode: Example: x = sin (y) Differentiate this function with respect to x on both sides. Solve for dy/dx. 15 Mar 2022 ... We will discuss the derivative notations. I find it really helps to explain to calculus 1 students the difference between the notations d/dx ...May 2, 2015 · The symbol. dy dx. means the derivative of y with respect to x. If y = f(x) is a function of x, then the symbol is defined as. dy dx =limh→0 f(x + h) − f(x) h. and this is is (again) called the derivative of y or the derivative of f. Note that it again is a function of x in this case. Nov 23, 2023 · Dy dx is the derivative of y with respect to x, while dx dy is the derivative of x with respect to y. The two operations have different properties and can be used for different purposes. For example, dy dx is often used to calculate the slope of a graph, while dx dy is more commonly used to calculate changes in the magnitude of a function over ... Using the conventional "integral" notation for antiderivatives, we simply look to the previous section to see how to reverse the chain rule: ∫(f ∘ g) ′ (x)dx = (f ∘ g)(x) + C. The key idea when using u -substitution to integrate (i.e. anti-differentiate) is to isolate a part of the function (the " u " part) that:Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...15 Mar 2022 ... We will discuss the derivative notations. I find it really helps to explain to calculus 1 students the difference between the notations d/dx ... This calculus video tutorial provides a basic introduction into implicit differentiation. it explains how to find dy/dx and evaluate it at a point. It also... Differentiation of a function is finding the rate of change of the function with respect to another quantity. f. ′. (x) = lim Δx→0 f (x+Δx)−f (x) Δx f ′ ( x) = lim Δ x → 0. . f ( x + Δ x) − f ( x) Δ x, where Δx is the incremental change in x. The process of finding the derivatives of the function, if the limit exists, is ...由于dy/dx定义的出发点，这个符号是一个整体，而不是一个可以拆开的东西。 微分形式、流形等等概念依然十分重要：之所以定义这些概念，是因为我们想在各种各样千奇百怪的几何上继续愉快地微积分；它们的定义也自然的包含了一元函数的情况——事实上 ...f (x) Free ordinary differential equations (ODE) calculator - solve ordinary differential equations (ODE) step-by-step.Wolfram|Alpha is a great resource for determining the differentiability of a function, as well as calculating the derivatives of trigonometric, logarithmic, exponential, polynomial and many other types of mathematical expressions. Differentiation has many applications within physics, trigonometry, analysis, optimization and other fields.Implicit differentiation can help us solve inverse functions. The general pattern is: Start with the inverse equation in explicit form. Example: y = sin −1 (x) Rewrite it in non-inverse …Free implicit derivative calculator - implicit differentiation solver step-by-step.Find dy/dx y=x^(cos(x)) Step 1. Differentiate both sides of the equation. Step 2. The derivative of with respect to is . Step 3. Differentiate the right side of the equation. Tap for more steps... Step 3.1. Use the properties of logarithms to simplify the differentiation. Tap for more steps... Step 3.1.1.Integrating both sides. [Math Processing Error] [Math Processing Error] [Math Processing Error] Answer link. THe solution is y=e^ (-cosx+C) This is a first order differential equation of the form N (y)dy=M (x)dx dy/dx=ysinx dy/y=sinxdx Integrating both sides intdy/y=intsinxdx lny=-cosx+C y=e^ (-cosx+C)Learn how to do a derivative using the dy/dx notation, also called Leibniz's notation, instead of limits. See the formulas, examples and explanations for different functions and situations. Try it on a function and see the result.Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange작성자Klein 작성시간10.11.06 오히려 differential form은, 미적분학의 기본 정리 (y = f (x)일 때, int_a^b dy/dx dx = f (b)-f (a))를 임의의 차원으로 확장시키려는 결과의 산물입니다. 그리고 differential form을 이용한 Stokes 정리 등의 …Solve the differential equation: dy/dx = [x+y cosx/1+sinx)] cbse; class-12; Share It On Facebook Twitter Email. Play Quiz Game > 1 Answer +1 vote . answered Apr 21, 2019 by Bhawna (69.0k points) selected Apr 21, 2019 by Farhat . Best answer. Comparing with linear D.E form ← Prev ...The slope of the dashed line is given by the ratio `(Delta y)/(Delta x).` As `Delta x` gets smaller, that slope becomes closer to the actual slope at P, which is the "instantaneous" ratio `dy/dx`. That is, `lim_(Delta x->0) (Delta y)/(Delta x)=dy/dx` See Slope of a tangent for some background on this.This calculus video tutorial provides a basic introduction into implicit differentiation. it explains how to find dy/dx and evaluate it at a point. It also... The live dYdX (ethDYDX) price today is $3.52 USD with a 24-hour trading volume of $79,602,436 USD. We update our ETHDYDX to USD price in real-time. dYdX (ethDYDX) is down 4.26% in the last 24 hours. The current CoinMarketCap ranking is #97, with a live market cap of $1,039,471,632 USD. It has a circulating supply of 295,616,430 ETHDYDX coins ... Presentasi berjudul: "Diferensial dx dan dy."— Transcript presentasi: ... 6 Dalam tabel ini v adalah fungsi x. ... Download ppt "Diferensial dx dan dy." ..... A very interesting calculus 1 derivative notation problem: is dy/dx the same as 1/(dx/dy)? -----👉 Subscribe: http://bit.ly/bprpfast👉 Support... Differentiate both sides of the equation. d dx (y) = d dx (3x) d d x ( y) = d d x ( 3 x) The derivative of y y with respect to x x is y' y ′. y' y ′. Differentiate the right side of the equation. Tap for more steps... 3 3. Reform the equation by setting the left side equal to …What it is: dy/dx is a fraction with a condition built in! The condition is that dy is the change in y ( which we call dy ) CAUSED by a change in x ( dx ). The dy is dependent on the dx. A better way to think of dy/dx is to think of it as a function, instead, where you would plug in a dx, get an intermediate dy, and then return the ratio of dy/dx.A first order Differential Equation is Homogeneous when it can be in this form: dy dx = F ( y x ) We can solve it using Separation of Variables but first we create a new variable v = y x. v = y x which is also y = vx. And dy dx = d (vx) dx = v dx dx + x dv dx (by the Product Rule) Which can be simplified to dy dx = v + x dv dx.If you’ve ever experienced the frustration of a car remote that doesn’t work when you need it most, it may be time to replace the battery. One of the most obvious signs that your c...Some may be nostalgic for the long lines outside sneaker stores. In its battle to take a shred of market share—and design swagger—from Nike, Adidas may have no greater ally than th... Enter the implicit function in the calculator, for this you have two fields separated by the equals sign. The functions must be expressed using the variables x and y. Select dy/dx or dx/dy depending on the derivative you need to calculate. Press the “Calculate” button to get the detailed step-by-step solution. If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x" . Differentiating x to the power of something. 1) If y = x n, dy/dx = nx n-1. 2) If y = kx n, dy/dx = nkx n-1 (where k is a constant- in other words a ... Find dy/dx y=cos(3x) Step 1. Differentiate both sides of the equation. Step 2. The derivative of with respect to is . Step 3. Differentiate the right side of the equation. Tap for more steps... Step 3.1. Differentiate using the chain rule, which states that is where and . …Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly.dy/dx, d/dx, and dy/dt - Derivative Notations in Calculus. This calculus video tutorial discusses the basic idea behind derivative notations such as dy/dx, d/dx, dy/dt, … Calculus. Find dy/dx y=1/x. y = 1 x y = 1 x. Differentiate both sides of the equation. d dx (y) = d dx ( 1 x) d d x ( y) = d d x ( 1 x) The derivative of y y with respect to x x is y' y ′. y' y ′. Differentiate the right side of the equation. Tap for more steps... Find dy/dx y=sin(cos(x)) Step 1. Differentiate both sides of the equation. Step 2. The derivative of with respect to is . Step 3. Differentiate the right side of the equation. Tap for more steps... Step 3.1. Differentiate using the chain rule, which states that is where and . Tap for more steps...Differentiate both sides of the equation. d dx (y) = d dx (3x) d d x ( y) = d d x ( 3 x) The derivative of y y with respect to x x is y' y ′. y' y ′. Differentiate the right side of the equation. Tap for more steps... 3 3. Reform the equation by setting the left side equal to …Using the conventional "integral" notation for antiderivatives, we simply look to the previous section to see how to reverse the chain rule: ∫(f ∘ g) ′ (x)dx = (f ∘ g)(x) + C. The key idea when using u -substitution to integrate (i.e. anti-differentiate) is to isolate a part of the function (the " u " part) that:27 Mar 2021 ... Here i solve the question d/dx (dy/dx)square. Hope it helps and is interesting.29 Oct 2020 ... Tutorial TURUNAN Menentukan dy/dx,d²y/dx²,d³y/dx³ Fungsi Aljabar (Req.via Telegram) - Matematika SMA. 35K views · 3 years ago ...more ...derivative (dy/dx)*(dx/dy) en. Related Symbolab blog posts. High School Math Solutions – Derivative Calculator, the Chain Rule . In the previous posts we covered the basic derivative rules, trigonometric functions, logarithms and exponents... Enter a …This video explains the difference between dy/dx and d/dxJoin this channel to get access to perks:https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/jo... Here, d d x serves as an operator that indicates a differentiation with respect to x . This notation also allows us to directly express the derivative of an expression without using a function or a dependent variable. For example, the derivative of x 2 can be expressed as d d x ( x 2) . When you had dy/dx = -x/y(e^(x^2)), it was essentially the derivative of y given. To reverse this derivative, we integrate, as we know that doing so gives us back our original function y. Also, no need to apologize for asking a lot of questions. The more you ask, the better understanding you gain!derivative (dy/dx)*(dx/dy) en. Related Symbolab blog posts. High School Math Solutions – Derivative Calculator, the Chain Rule . In the previous posts we covered the basic derivative rules, trigonometric functions, logarithms and exponents... Enter a … If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x" . Differentiating x to the power of something. 1) If y = x n, dy/dx = nx n-1. 2) If y = kx n, dy/dx = nkx n-1 (where k is a constant- in other words a ... Find the particular solution of differential equation: dy/dx=(−x+ycosx)/(1+sinx) given that y=1 when x=0 . CBSE Science (English Medium) Class 12. Question Papers 1978. Textbook Solutions 24549. MCQ Online Mock Tests 43. Important …
Using the conventional "integral" notation for antiderivatives, we simply look to the previous section to see how to reverse the chain rule: ∫(f ∘ g) ′ (x)dx = (f ∘ g)(x) + C. The key idea when using u -substitution to integrate (i.e. anti-differentiate) is to isolate a part of the function (the " u " part) that:. Best satin pillowcase
The slope of the dashed line is given by the ratio `(Delta y)/(Delta x).` As `Delta x` gets smaller, that slope becomes closer to the actual slope at P, which is the "instantaneous" ratio `dy/dx`. That is, `lim_(Delta x->0) (Delta y)/(Delta x)=dy/dx` See Slope of a tangent for some background on this.8 Dec 2019 ... Comments1 · 3 to (x/2) = 12, many don't know where to start · 2 times (10 + 16 / 2 x 8) = ? BECAREFUL, many will do this in the WRONG ORDER!History and usage. The differential was first introduced via an intuitive or heuristic definition by Isaac Newton and furthered by Gottfried Leibniz, who thought of the differential dy as … Gottfried Wilhelm von Leibniz (1646–1716), German philosopher, mathematician, and namesake of this widely used mathematical notation in calculus. In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small (or ... Lordstown Motors said it will end production of the Endurance EV truck in the near future after losing funding from partner Foxconn. Beleaguered EV company Lordstown Motors seemed ...I thought about moving the $-x\frac{dy}{dx}$ over to the RHS and then group it under the common variable $\frac{dy}{dx}$ but the question was under the 'separable differential' section in my textbook so I don't think it's the correct method. ordinary-differential-equations; Share. Cite.d/dxは「文字xで微分する」ことを表す. lecturer_avatar. d/dxは，簡単に言うと， 「文字xで微分する」 操作を表す記号です。同様に，d/dyは，「文字yで微分する」 操作を ...Antibiotics aren’t doing what they’re supposed to do anymore. You know, kill infections. Since Alexander Fleming invented penicillin 75 years ago, nearly all bacteria have mutated ...Differentiation of a function is finding the rate of change of the function with respect to another quantity. f. ′. (x) = lim Δx→0 f (x+Δx)−f (x) Δx f ′ ( x) = lim Δ x → 0. . f ( x + Δ x) − f ( x) Δ x, where Δx is the incremental change in x. The process of finding the derivatives of the function, if the limit exists, is ... Or sometimes the derivative is written like this (explained on Derivatives as dy/dx): dy dx = f(x+dx) − f(x) dx The process of finding a derivative is called "differentiation". This video explains the difference between dy/dx and d/dxJoin this channel to get access to perks:https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/jo...7 Dec 2020 ... Learn How to Use Logarithmic Differentiate to Find the Derivative dy/dx If you enjoyed this video please consider liking, sharing, ...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange dy/dx is differentiating an equation y with respect to x. d/dx is differentiating something that isn't necessarily an equation denoted by y. So for example if you have y=x 2 then dy/dx is the derivative of that, and is equivalent to d/dx (x 2) And the answer to both of them is 2x. [deleted] The live dYdX (ethDYDX) price today is $3.52 USD with a 24-hour trading volume of $79,602,436 USD. We update our ETHDYDX to USD price in real-time. dYdX (ethDYDX) is down 4.26% in the last 24 hours. The current CoinMarketCap ranking is #97, with a live market cap of $1,039,471,632 USD. It has a circulating supply of 295,616,430 ETHDYDX coins ... dy/dxを単なる微分のとしてしか使わないこととして習いますが、 式を眺めるときには、無限小と思って解釈するとよくわかるようになります。 ちなみに、積分の記号で最後にdxなんてものがついていますが、 このdxも微分にでてくるdxと同じものだと思 … f (x) Free implicit derivative calculator - implicit differentiation solver step-by-step. We can't know for sure exactly how we're going to die, but some ways of going are more common than others. The National Safety Council has calculated the probability of dying from ...The derivative of a polar function r (θ) is dr/dθ. In this case, it is dr/dθ = -2sin (θ). If you plot r (θ) on the way that θ is on the horizontal axis and r is on the vertical axis, you get a simple cosine plot. But you can plot the r (θ) function on the (x,y) plane, in polar coordinates (r is the distance from origin and theta is the ....