Differentiate both sides of the equation.

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

Evaluate .

Differentiate using the Product Rule which states that is where and .

Rewrite as .

Differentiate using the Power Rule which states that is where .

Move to the left of .

Evaluate .

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

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 .

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

Simplify.

Add and .

Reorder terms.

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

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

Reorder factors in .

Subtract from both sides of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

Replace with .

Find dy/dx x^2y-e^y-9=0