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 .

The derivative of with respect to is .

Replace all occurrences of with .

Differentiate.

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

Differentiate using the Power Rule which states that is where .

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 .

Reorder the factors of .

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

Simplify .

Multiply and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Move all terms containing to the left side of the equation.

Subtract from both sides of the equation.

Simplify the left side of the equation.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Apply the distributive property.

Apply the distributive property.

Remove unnecessary parentheses.

Multiply both sides of the equation by .

Remove parentheses.

Multiply by .

Add to both sides of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Replace with .

Find dy/dx y = natural log of x^2+y^2