Differentiate both sides of the equation.

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 .

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

Differentiate using the Power Rule.

Differentiate using the Power Rule which states that is where .

Multiply by .

Rewrite as .

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

Evaluate .

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 .

Evaluate .

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

Rewrite as .

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

Combine and .

Move all terms containing to the left side of the equation.

Add to both sides of the equation.

To write as a fraction with a common denominator, multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Apply the distributive property.

Rewrite using the commutative property of multiplication.

Reorder factors in .

Multiply both sides of the equation by .

Remove parentheses.

Multiply by .

Subtract from both sides of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Combine into one fraction.

Move the negative in front of the fraction.

Combine the numerators over the common denominator.

Simplify the numerator.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Simplify with factoring out.

Factor out of .

Factor out of .

Factor out of .

Rewrite negatives.

Rewrite as .

Move the negative in front of the fraction.

Replace with .

Find dy/dx e^(x/y)=5x-y