# Partial Derivatives

• Jun 18th 2011, 06:34 PM
spruancejr
Partial Derivatives
Let $h(x,y))= f(\frac{x+y}{x-y})$ where f is a $C^1$ class function.

Find $\frac{dh}{dx}$ and $\frac{dh}{dy}$

I'm having trouble understanding the relationship between the h and f and what functions are contained within each.
• Jun 18th 2011, 08:36 PM
TKHunny
Re: Partial Derivatives
$\frac{dh}{dx}\;=\;\frac{dh}{df}\cdot\frac{df}{dx}$

In the old days, back in Calculus I, we called this the chain rule.

We don't know much about f, so just go with f'. That should do it.
• Jun 19th 2011, 06:43 AM
HallsofIvy
Re: Partial Derivatives
Well, since this is not Calculus I, those should be partial derivatives: If we let $u(x,y)= \frac{x+ y}{x- y}$,
$\frac{\partial h}{\partial x}= \frac{df}{du}\frac{\partial u}{\partial x}$
$\frac{\partial h}{\partial y}= \frac{df}{du}\frac{\partial u}{\partial y}$

Yes, you can write "df/du" as just f '.
• Jun 19th 2011, 03:46 PM
TKHunny
Re: Partial Derivatives
I think I've never coded a "partial" in LaTeX. That's weird. I wonder how I managed to miss that...

$\frac{\partial y}{\partial x}$

Okay, I think I have it, now.