The derivative of x^π (x to the power pi) is equal to πx^{π-1}. In this post, we will learn how to differentiate x to the power pi with respect to x.

The derivative of x^{π} is denoted by d/dx (x^{π}) or (x^{π})’. Its formula is given by

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

## Derivative of x to the power pi

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

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

**Answer:**

Note that the number π is an irrational number, so it is a constant. Its value is approximately equal to $\dfrac{22}{7}$.

So, to find the derivative of x^{π}, we can apply the power rule of derivatives. The rule says that the derivative of x^{n} is equal to nx^{n-1}. That is,

$\dfrac{d}{dx}$(x^{n}) = nx^{n-1}.

Put n=π. Thus, we get that

$\dfrac{d}{dx}$(x^{π}) = π x^{π-1}.

So the derivative of x^{π} (x power π) is equal to π x^{π-1}, and this is proved by the power rule of derivatives.

## Question-Answer

Question: What is the derivative of 2^{π} (2 to the power pi). |

**Answer:**

As both 2 and π are constants, we conclude that 2^{π} is also a constant.

We know that the derivative of a constant is zero, that is,

$\dfrac{d}{dx}$ (constant) = 0.

So, $\dfrac{d}{dx}(2^\pi)=0$.

Thus, the derivative of 2 to the power pi is equal to 0.

**More Derivatives:**

## FAQs

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

**Answer:** The derivative of x^π (x raised to the power pi) is equal to π x^{π-1}.