Problem

Let y = ln(x² + y²). Find y'.

Solution

We can solve this by using the chain rule and implicit differentiation.

Solve for y'.

Another way to solve it

We can also start by separating the variables, putting the y's on one side of the equation and the x's on the other.

First, exponentiate both sides.

Now differentiate implicitly

and solve for dy/dx.

Since e^y = x² + y², these two solutions are the same.