Use to rewrite as .

Differentiate both sides of the equation.

The derivative of with respect to is .

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 .

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 .

Combine fractions.

Move the negative in front of the fraction.

Combine and .

Move to the denominator using the negative exponent rule .

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

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

Add and .

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

Simplify terms.

Combine and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Differentiate using the Power Rule which states that is where .

Combine fractions.

Combine and .

Multiply by .

Combine and .

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

Replace with .

Find ds/dy s = square root of 2x^2+6y^2