The differentiation of e^cotx is equal to -cosec^{2}x e^{cotx}. In this post, we will learn how to differentiate e to the power cotx with respect to x.

The following two formulas will be used to find the derivative of e^{cotx}.

- d/dx(cotx) = -cosec
^{2}x. - log
_{a}a^{k }=k.

Now, we will learn to find the derivative of e to the power cotx with respect to x.

**How to Find the derivative of e**^{cotx}

**How to Find the derivative of e**

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

**Solution:**

Let y= e^{cotx}

Taking natural logarithms on both sides, we get that (natural logarithm means the logarithm with base e, i.e. log_{e})

log y = cotx

**[Here we have used the above formula 2**]

Now, differentiate both sides with respect to x. This will give us

$\dfrac{1}{y} \dfrac{dy}{dx}$ = -cosec^{2}x, **by the above formula 1**.

⇒ $\dfrac{dy}{dx}$ = -y cosec^{2}x

Now put back the value of y, that is, y=e^{cotx}. Therefore, we obtain that

$\dfrac{d}{dx}$(e^{cotx}) = – e^{cotx }cosec^{2}x.

**Thus, the differentiation of e ^{cotx} with respect to x is equal to -e^{cotx} cosec^{2}x.**

**ALSO READ:**

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

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

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

Differentiate e^{tanx}: The derivative of e^{tanx} is e^{tanx} sec^{2}x.

## FAQs

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

Answer: The derivative of e^cotx is equal to -cosec^{2}x e^{cotx}.

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

Answer: If y=e^{cotx}, then dy/dx = -cosec^{2}x e^{cotx}.