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 Power Rule which states that is where .

Replace all occurrences of with .

Rewrite as .

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.

Add and .

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.

Add and .

Multiply by .

Simplify.

Apply the distributive property.

Simplify the numerator.

Combine the opposite terms in .

Subtract from .

Add and .

Multiply by .

Add and .

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

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)