AP Calculus ABhardmcq1 pt

If $f(x)=\sin(\cos(x^2))$ , then $f'(x)=$

-2x\sin(x^2)\cos(\cos(x^2))

2x\sin(x^2)\cos(\cos(x^2))

-2x\sin(x^2)\sin(\cos(x^2))

-\sin(x^2)\cos(\cos(x^2))

Explanation

Core Concept

Layer the chain rule three times: $\cos(\cos(x^2))$ for sine, then $-\sin(x^2)$ , then $2x$ for $x^2$ . The product is $-2x\sin(x^2)\cos(\cos(x^2))$ .

Correct Answer

A $-2x\sin(x^2)\cos(\cos(x^2))$

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Practice Unit 3: Differentiation: Composite, Implicit, and Inverse Functions Questions →

If f(x)=sin⁡(cos⁡(x2))f(x)=\sin(\cos(x^2))f(x)=sin(cos(x2)), then f′(x)=f'(x)=f′(x)=

Explanation

Core Concept

Correct Answer

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