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

Let , take the natural logarithm of both sides .
Expand by moving outside the logarithm.
Differentiate the expression using the chain rule, keeping in mind that is a function of .
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 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)