Differentiate both sides of the equation.

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

Evaluate .

Differentiate using the Power Rule which states that is where .

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

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Evaluate .

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 .

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

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Combine and .

Move to the denominator using the negative exponent rule .

Rewrite the expression using the negative exponent rule .

Simplify.

Multiply 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.

Simplify each term.

Combine and .

Move to the left of .

Subtract from both sides of the equation.

Multiply both sides of the equation by .

Simplify .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Move the negative in front of the fraction.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Replace with .

Find dy/dx x^(2/3)+y^(2/3)=4