Differentiate both sides of the equation.

The derivative of with respect to is .

By the Sum Rule, the derivative of with respect to is .

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

Evaluate .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

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

Differentiate using the Power Rule which states that is where .

Multiply by .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Reform the equation by setting the left side equal to the right side.

Replace with .

Find dz/dy z=x^y+ natural log of xy