# Evaluate $\dfrac{d}{dx}{\,\big(x^x\big)}$

Let $x$ be a variable. The variable $x$ raised to the power $x$ forms a special function $x^x$.

The derivative of the $x$-th power of $x$ with respect to $x$ is written in mathematics as follows.

$\dfrac{d}{dx}{\,\big(x^x\big)}$

The function is not an exponential function or a power function but it is a combination of both. Hence, the differentiation of this special function cannot be calculated directly and it requires some methods to find its derivative.

## Proofs

The differentiation of this exponential power function can be evaluated in the following two methods.

### Log method

Learn how to find the differentiation of $x$ to the $x$-th power with respect to $x$ by using logarithmic system.

### Limits method

Learn how to calculate the derivative of the $x$-th power of $x$ with respect to $x$ from the first principle of differentiation.

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