Question

y= e^log sin x then dy/dx=

Answer 1

ANSWER:

$\cot(x) {e}^{ ln( \sin(x) ) }$

STEP-BY-STEP-VERIFICATION :-

$\frac{dy}{x} \\ = > \: \: \frac{d}{dx} {e}^{ ln( \sin(x) ) } \\ = > \: \: {e}^{ln( \sin(x)) } \frac{d}{dx} ln( \sin(x)) \\ = > \: \: {e}^{ ln( \sin(x) ) } \frac{1}{ \sin(x) } \frac{d}{dx} \sin(x) \\ = > \: \: {e}^{ ln( \sin(x) ) } \frac{1}{ \sin(x) } \cos(x) \\ = > \: \: \cot(x) {e}^{ ln( \sin(x) ) }$