How do you partial differentiate with respect to a function of multiple variables of even more variables inside an operation?

Question

For instance, if I have an expression $f(w,t)$ = $\sqrt{w^{2}+t^{2}}$, but then additionally $w$ is some function of $x$ and $y$, $w(x,y)$ and $t$ is $t(x,y)$, then how would I differentiate $f$ with respect to $x$ or $y$?

Answer 1

$$\frac{\partial f}{\partial x}=\frac{\partial f}{\partial w}\cdot\frac{\partial w}{\partial x}+\frac{\partial f}{\partial t}\cdot\frac{\partial t}{\partial x}$$