Section 14.5 Chain Rule

Assume that all the given functions are differentiable. If \(z = \frac{1}{y}[f(ax + y) + g(ax - y)]\), show that \[ \frac{\partial}{\partial x}\left(y^2 \frac{\partial z}{\partial x}\right) = a^2 \frac{\partial}{\partial y}\left(y^2 \frac{\partial z}{\partial y}\right) \]