Partial derivative of a functional

Question

I have a functional W[V(x,y)], so what is the partial derivative $\partial W/\partial x$? Thanks in advance.

Answer 1

Use the chain rule: the dependencies are $x \to V \to W$ so that $$\frac{\partial W}{\partial x} = \frac{dW}{dV} \frac{\partial V}{\partial x}.$$