Assertion (A): For $f(x) = \sin(x^{2})$ , $f'(-x) = -f'(x)$ for every $x$ .
Reason (R): The derivative of a differentiable odd function is an even function.

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 B

Correct answer: B

A is true: $f'(x) = 2x\cos(x^{2})$ , and $f'(-x) = -2x\cos(x^{2}) = -f'(x)$ .
R is true (differentiate $g(-x) = -g(x)$ by the chain rule), but $\sin(x^{2})$ is even, so A comes from the rule for even functions, not from R.

Worth noting

R speaks of odd functions; $\sin(x^{2})$ is even, so R, though true, is not why A holds.

Concept: Derivatives of even and odd functions
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe chain rule

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Assertion (A): For f(x)=sin⁡(x2)f(x) = \sin(x^{2})f(x)=sin(x2), f′(−x)=−f′(x)f'(-x) = -f'(x)f′(−x)=−f′(x) for every xxx.Reason (R): The derivative of a differentiable odd function is an even function.

Explanation

Assertion (A): For $f(x) = \sin(x^{2})$ , $f'(-x) = -f'(x)$ for every $x$ .
Reason (R): The derivative of a differentiable odd function is an even function.