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Single Variable Calculus

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Difficult

Logarithmic Differentiation with sin($x$) and ln($x$) Functions

SVCALC-EDJR8E

Find derivative of the function $y=\sin(x)^{\ln(x)}$.

A

$\ln(x)\sin(x)^{\ln(x)-1}$

B

$\ln(x)\sin(x)^{\ln(x)-1} \cos(x)$

C

$(\cfrac{ln(\sin(x))}{x}+\ln(x)\cot(x))\sin(x)^{\ln(x)}$

D

$(\cfrac{ln(\sin(x))}{x}+\cfrac{\ln(x)}{\sin(x)})\sin(x)^{\ln(x)}$