The differentiation of e^sinx is equal to cosx e^{sinx}. In this post, we will learn how to differentiate e^sinx with respect to x.

Let us find the derivative of e^{sinx} with respect to x.

**Find the derivative of e**^{sinx}

^{sinx}

**Question**: How to differentiate e^{sinx}?

**Solution:**

Let y= e^{sinx}

Taking natural logarithms i.e. log_{e} both sides, we get that

log y = sinx as we know that log_{e}e^{k} =k.

Now, differentiate both sides with respect to x. So we get that

$\dfrac{1}{y} \dfrac{dy}{dx}$ = cosx

⇒ $\dfrac{dy}{dx}$ = y cosx

Putting the value of y, that is, y=e^{sinx}, we get that

$\dfrac{d}{dx}$(e^{sinx}) = e^{sinx} cosx.

**Thus, the differentiation of e ^{sinx} with respect to x is equal to e^{sinx} cosx.**

**Video solution:**

**ALSO READ:**

Derivative of arc(cotx): The derivative of arc(cotx) is -1/(1+x^{2}).

## FAQs

### Q1: What is the derivative of e^{sinx}?

Answer: The derivative of e^sinx is equal to cosx e^{sinx}.

### Q2: If y=e^{sinx}, then find dy/dx?

Answer: If y=e^{sinx}, then dy/dx = cosx e^{sinx}.