Differentiate both sides of the equation.

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 Product Rule which states that is where and .

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 Power Rule which states that is where .

Replace all occurrences of with .

Rewrite as .

Multiply by .

Move to the left of .

Evaluate .

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

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

Differentiate using the Power Rule which states that is where .

Rewrite as .

Move to the left of .

Simplify.

Apply the distributive property.

Apply the distributive property.

Combine terms.

Multiply by .

Multiply by .

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.

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

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 .

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Simplify each term.

Move the negative in front of the fraction.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Multiply and .

Reorder the factors of .

Combine the numerators over the common denominator.

Simplify the numerator.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Multiply by .

Multiply by .

Simplify with factoring out.

Factor out of .

Factor out of .

Factor out of .

Simplify the expression.

Rewrite as .

Move the negative in front of the fraction.

Replace with .

Find dx/dy 2x^3y+3xy^3=5