The derivative of x^e (x to the power e) is equal to ex^{e-1}. Here we will learn to differentiate x^e with respect to x. The derivative of x^{e} is denoted by d/dx (x^{e}) or (x^{e})’. Its formula is given by

$\dfrac{d}{dx}(x^e)=ex^{e-1}$.

## Derivative of x to the power e

**Question:** Find the derivative of x^{e}, that is, Find

$\dfrac{d}{dx}(x^e)$.

**Answer:**

As the number e is an irrational number, so it is a constant, whose value lies between 2 and 3.

Thus, we can apply the power rule of derivatives: $\dfrac{d}{dx}$(x^{n}) = nx^{n-1} in order to get the derivative of x^{e}.

Applying this formula, we obtain that

$\dfrac{d}{dx}$(x^{e}) = ex^{e-1}.

So the derivative of x^{e} is equal to ex^{e-1}, and this is obtained by the power rule of derivatives.

## Question-Answer

Question: Find the derivative of $x^{e^2}$ (x to the power e^{2}). |

**Answer:**

As e^{2} is a constant, by the power rule of derivatives,

$\dfrac{d}{dx}(x^{e^2})=e^2 x^{e^2-1}$.

So the derivative of x to the power e^2 is equal to $e^2 x^{e^2-1}$.

**More Derivatives:**

What is the Derivative of e^{1/x}?

## FAQs

### Q1: What is the derivative of x^e?

**Answer:** The derivative of x^e is equal to ex^{e-1}.