Differentiate both sides of the equation.

Differentiate using the Power Rule which states that is where .

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

To apply the Chain Rule, set as .

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

Replace all occurrences of with .

Rewrite as .

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

Rewrite the equation as .

Divide each term by and simplify.

Divide each term in by .

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Replace with .

Find dx/dy y=19^x