Find the derivative of a function where the variable appears in both the base and the exponent using logarithmic differentiation.

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Derivative of x to the Power of x

Logarithmic and exponential functions core

Find \(D_x(x^x)\).

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What you need first

The product rule for differentiation
The chain rule for differentiation
The derivative of the natural logarithm
Properties of logarithms

What this problem tests

Tests the ability to recognize when standard derivative rules fail and logarithmic differentiation is required, as well as the application of the product and chain rules.

This is a classic calculus problem often used to introduce logarithmic differentiation.

Derivative of x to the Power of x

What you need first

What this problem tests

More on Logarithmic and exponential functions