Assertion (A): For x^2 + y^2 = 4, dy/dx = -x/y. Reason (R): Differentiating y^2 with respect to x gives 2ydy/dx.

Question 39

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Assertion (A): For $x^2 + y^2 = 4$ , $\frac{dy}{dx} = -\frac{x}{y}$ .
Reason (R): Differentiating $y^2$ with respect to $x$ gives $2y\frac{dy}{dx}$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

R is the chain rule, with $y$ a function of $x$ , so it is true.
Using it, $2x + 2y\frac{dy}{dx} = 0$ and $\frac{dy}{dx} = -\frac{x}{y}$ : A is true, and R is the step that gives it.

Concept: Differentiating an implicit function
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsImplicit functions

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Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Assertion (A): For x2+y2=4x^2 + y^2 = 4x2+y2=4, dydx=−xy\frac{dy}{dx} = -\frac{x}{y}dxdy​=−yx​.Reason (R): Differentiating y2y^2y2 with respect to xxx gives 2ydydx2y\frac{dy}{dx}2ydxdy​.

Explanation

Assertion (A): For $x^2 + y^2 = 4$ , $\frac{dy}{dx} = -\frac{x}{y}$ .
Reason (R): Differentiating $y^2$ with respect to $x$ gives $2y\frac{dy}{dx}$ .