# Differentiate multivariable function with respect to another function

• December 19th 2012, 11:15 AM
Essa
Differentiate multivariable function with respect to another function
Given a function of the form f(x,y) = (a-b x)^2 - (c - d y)^2, how can I tell how does f change when (x-y) change?

• December 19th 2012, 08:08 PM
chiro
Re: Differentiate multivariable function with respect to another function
Hey Essa.

Do you know about directional derivatives?
• December 20th 2012, 07:02 PM
hollywood
Re: Differentiate multivariable function with respect to another function
I'm a little weak on multi-variable calculus, but if g=x-y, can't you just do:

$\frac{df}{dg} = \frac{df/dx}{dg/dx} + \frac{df/dy}{dg/dy}$

- Hollywood