Let , take the natural logarithm of both sides .

Expand by moving outside the logarithm.

Differentiate the left hand side using the chain rule.

Differentiate the right hand side.

Differentiate .

Since is constant with respect to , the derivative of with respect to is .

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.

Rewrite the expression.

Differentiate using the Power Rule which states that is where .

Multiply by .

Simplify.

Apply the distributive property.

Multiply by .

Reorder terms.

Isolate and substitute the original function for in the right hand side.

Simplify by moving inside the logarithm.

Apply the distributive property.

Reorder factors in .

Use Logarithmic Differentiation to Find the Derivative y=x^(2x)