# Find the Derivative - d/dx x^x

Rewrite as .

Expand by moving outside the logarithm.

To apply the Chain Rule, set as .

Differentiate using the Exponential Rule which states that is where =.

Replace all occurrences of with .

Differentiate using the Product Rule which states that is where and .

The derivative of with respect to is .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Differentiate using the Power Rule which states that is where .

Multiply by .

Apply the distributive property.

Multiply by .

Reorder terms.

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