Find the Derivative - d/dx x^x

Find the Derivative - d/dx x^x
Use the properties of logarithms to simplify the differentiation.
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Rewrite as .
Expand by moving outside the logarithm.
Differentiate using the chain rule, which states that is where and .
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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 .
Differentiate using the Power Rule.
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Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Differentiate using the Power Rule which states that is where .
Multiply by .
Simplify.
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Apply the distributive property.
Multiply by .
Reorder terms.
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