# What is the differentiation of $$e^{sinx}$$ ?

## Solution :

Let y = $$e^{sinx}$$. Putting u = sinx , we get

y = $$e^u$$ and u = sinx

$$\therefore$$  $$dy\over du$$ = $$e^u$$ and $$du\over dx$$ = cosx

Now, $$dy\over dx$$ = $$dy\over du$$ $$\times$$ $$du\over dx$$

$$\implies$$ $$dy\over dx$$ = $$e^u$$cosx = $$e^{sinx}$$cosx

Hence, the differentiation of $$e^{sinx}$$ with respect to x is $$e^{sinx}$$cosx.

### Questions for Practice

What is the differentiation of cosx sinx ?

What is the differentiation of sin square x or $$sin^2x$$ ?

What is the differentiation of 1/sinx ?

What is the differentiation of $$sin x^2$$ ?

What is the differentiation of log sin x ?