# Find dy/dx x^(2/3)+y^(2/3)=4 Differentiate both sides of the equation.
Differentiate the left side 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.
Solve for .
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 .
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