# partial derivatives of functions wrt to another function?

• Feb 25th 2013, 06:59 PM
knkumar
partial derivatives of functions wrt to another function?
I came across this problem in a text I am using currently and was confused by the notation and am not sure of the answer

given a function $f = h(g_1, g_2, g_3)$
if $h=x^2 - yz$ and $f = h(x+y, y^2,x+z)$ then is it correct to apply the pointwise vector coordinate function and get $f = (x+y)^2 -y^2(x+z)$

This seemed like a trivial problem but the notation really confuses me.
• Feb 27th 2013, 09:37 AM
HallsofIvy
Re: partial derivatives of functions wrt to another function?
Quote:

Originally Posted by knkumar
I came across this problem in a text I am using currently and was confused by the notation and am not sure of the answer

given a function $f = h(g_1, g_2, g_3)$
if $h=x^2 - yz$ and $f = h(x+y, y^2,x+z)$ then is it correct to apply the pointwise vector coordinate function and get $f = (x+y)^2 -y^2(x+z)$

This seemed like a trivial problem but the notation really confuses me.

Yes, that exactly what the notation means: $f= h(x+ y, y^2, x+ z)= (x+y)^2- (y^2)(x+ z)$. The fact that x, y, z are used as "place holders" in both functions is irrelevant.
This is exactly the same as if it were $h(u, v, w)= u^2- vw$