Assertion (A): If y = x^3, then d^2y/dx^2 = (dy/dx)^2. Reason (R): d^2y/dx^2 is the derivative of dy/dx.

Question 71

MediumOriginal question

Assertion (A): If $y = x^3$ , then $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$ .
Reason (R): $\frac{d^2y}{dx^2}$ is the derivative of $\frac{dy}{dx}$ .

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 D

Correct answer: D

$\frac{dy}{dx} = 3x^2$ , so $\frac{d^2y}{dx^2} = 6x$ , while $\left(\frac{dy}{dx}\right)^2 = 9x^4$ : A is false.
R is the definition of the second derivative, so it is true.

Concept: The second derivative is not a square
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsSecond-order derivatives

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

Assertion (A): If y=x3y = x^3y=x3, then d2ydx2=(dydx)2\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2dx2d2y​=(dxdy​)2.Reason (R): d2ydx2\frac{d^2y}{dx^2}dx2d2y​ is the derivative of dydx\frac{dy}{dx}dxdy​.

Explanation

Assertion (A): If $y = x^3$ , then $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$ .
Reason (R): $\frac{d^2y}{dx^2}$ is the derivative of $\frac{dy}{dx}$ .