Differentiate both sides of the equation.

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

Evaluate .

Rewrite as .

Differentiate using the Power Rule which states that is where .

Evaluate .

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

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

Rewrite as .

Multiply by .

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Rewrite the expression using the negative exponent rule .

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.

Add to both sides of the equation.

Multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Simplify .

Combine and .

Move the negative in front of the fraction.

Multiply both sides of the equation by .

Combine and .

Replace with .

Find dy/dx 1/x+1/y=1