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

Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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.
Solve for .
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