Partial differential equations with multivariables

Question

If I have $u(x,t)=f(p(x,t))$ where f and p are functions.

What would the partials $du/dx$ and $du/dt$ be. I'd really appreciate the help thankk you.

Answer 1

Just apply the chain rule: $$\frac{\partial u}{\partial x}(x,t)=f'(p(x,t))\frac{\partial p}{\partial x}(x,t).$$