# Find dy/dx y^2=(x-1)/(x+1)

Differentiate both sides of the equation.
Differentiate the left side of the equation.
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 .
Differentiate the right side of the equation.
Differentiate using the Quotient Rule which states that is where and .
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Simplify the expression.
Multiply by .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Simplify the expression.
Multiply by .
Simplify.
Apply the distributive property.
Simplify the numerator.
Combine the opposite terms in .
Subtract from .
Multiply by .
Reform the equation by setting the left side equal to the right side.
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.
Divide by .
Simplify .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply and .
Reorder factors in .
Replace with .
Find dy/dx y^2=(x-1)/(x+1)