- #1
Yankel
- 390
- 0
Hello all,
I need some help with this chain rule problem.
\[F(x,y)=f\left (\frac{x-y}{x+y} \right )\]
It is known that:
f'(1)=20,f'(2)=30, f'(3)=40
and
\[f''(1)=5,f''(2)=6,f''(3))=7\]Find
\frac{\partial F}{\partial x}(2,-1)
and
\[\frac{\partial^2 F}{\partial x\partial y}\]The final answers should be -80 and 372.
I am less bothered with the final numbers (although would like to get there). It is the way that I am interested in. I was thinking to set t=x-y and s=x+y, but it got me stuck.
I need some help with this chain rule problem.
\[F(x,y)=f\left (\frac{x-y}{x+y} \right )\]
It is known that:
f'(1)=20,f'(2)=30, f'(3)=40
and
\[f''(1)=5,f''(2)=6,f''(3))=7\]Find
\frac{\partial F}{\partial x}(2,-1)
and
\[\frac{\partial^2 F}{\partial x\partial y}\]The final answers should be -80 and 372.
I am less bothered with the final numbers (although would like to get there). It is the way that I am interested in. I was thinking to set t=x-y and s=x+y, but it got me stuck.