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

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

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

^{cosx}

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

**Solution:**

Let y= e^{cosx}

Taking natural logarithms on both sides, we get that

logy = cosx [here we use the logarithm formula log_{e}e^{m} =m]

Differentiating both sides with respect to x, we get that

$\dfrac{1}{y} \dfrac{dy}{dx}$ = -sinx

⇒ $\dfrac{dy}{dx}$ = -y sinx

Now we put the value of y, that is, y=e^{cosx}. By doing so we obtain that

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

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

**Video solution:**

**ALSO READ:**

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

Derivative of e^{sinx}: The derivative of e^{sinx} is cosx e^{sinx}.

## FAQs

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

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

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

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