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AP® Calculus AB-BC

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Difficult

Chain Rule with Trigonometry

APCALC-UEJC0Z

Find $\lim \limits_{h \to 0} \frac{f'(x+h)-f'(x)}{h}$ if $f(x)=x^2 \cdot \sin (x^2)$.

A

$-4x^3 \sin(x^2)-4x^2 \cos(x^2) -4x \cos(x^2)+2\sin(x^2)$

B

$-4x^4\sin(x^2)+10x^2 \cos(x^2) +2\sin(x^2)$

C

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

D

$-2\sin(x^2)$