I'm not sure where to start, here. I can find no strategic examples in the text. Any ideas would be much appreciated. Thanks!Prove that if $\displaystyle h(u,v)=f(\sin u + \cos v)$, then $\displaystyle h_u\sin v+h_v\cos u=0$.
I'm not sure where to start, here. I can find no strategic examples in the text. Any ideas would be much appreciated. Thanks!Prove that if $\displaystyle h(u,v)=f(\sin u + \cos v)$, then $\displaystyle h_u\sin v+h_v\cos u=0$.
A good idea is to define $\displaystyle z=\sin u +\cos v$ , so $\displaystyle h(u,v)=f(z(u))$, and then:
$\displaystyle h_u=\frac{\partial f}{\partial z}\frac{\partial z}{\partial u}=\frac{\partial f}{\partial z}\cos u$
$\displaystyle h_v=\frac{\partial f}{\partial z}\frac{\partial z}{\partial v}=\frac{\partial f}{\partial z}(-\sin v)$
Well, now just put things together
Tonio