Question

Find the partial derivatives of the function.
w = sqrt(r^2+s^2+t^2)
w/r = ?
w/s = ?
w/t = ?

Answer 1

Use chain rule.

Answer 2

Consider it like: \[
w=\sqrt u, \quad u=r^2+s^2+t^2
\]Now: \[
\frac{\partial w}{\partial r}=\frac{d w}{d u}\frac{\partial u}{\partial r}
\]

Answer 3

We can start with \[
w'(u) = (\sqrt u)'=\frac 1{2\sqrt u}=\frac 1{2\sqrt {r^2+s^2+t^2}}
\]

Answer 4

@planetmonkey Can you find the rest?

Answer 5

You gotta find \[
\frac{\partial u}{\partial r},\frac{\partial u}{\partial s},\frac{\partial u}{\partial t}
\]

Answer 6

I have no idea

Answer 7

can you just plz type up the full explanation?