# Solve: d/dx (sin x)^2x

## Question:

Solve:

{eq}\frac{d}{dx} (sin\ x)^{2x} {/eq}

## Differentiation:

This question is from the differentiation and we have to find out the first order derivative and we will use logarithmic differentiation we find this.

{eq}\Rightarrow \ y=sin(x)^{2x}\\ \text{taking log both sides}\\ \Rightarrow \ \ln|y|=2x\ln|sin(x)|\\ \text{differentiate with respect to x}\\ \Rightarrow \ \frac{1}{y}y'=2x\frac{d}{dx}\ln|sin(x)|+\ln|sin(x)|\frac{d}{dx}2x\\ \Rightarrow \ y'=y(2xcot(x)+2\ln|sin(x)|)\\ \Rightarrow \ y'=sin(x)^{2x}(2xcot(x)+2\ln|sin(x)|)\\ {/eq}