Partial Differentiation (very simple mistake, I think)

[henryc09]

Homework Statement

[PLAIN]http://img408.imageshack.us/img408/7163/partialdifferent.jpg

So this means differentiate w.r.t y first, so I want dz/dy, and then w.r.t x right?

so I rearrange so that y=z³/3 + xz
and differentiate w.r.t z to get dy/dz, and then do 1 over this which i get as:

1/(z²+x)

and then differentiating this w.r.t x, I get
-1/(z²+x)²

which isn't quite right. Can anyone see where I've gone wrong? Thanks.

 

[vela]

You need to use the chain rule. Don't forget z still varies with x.

 

[rs1n]

You need to use the chain rule. Don't forget z still varies with x.

It may help to rewrite $z$ as $z(x,y)$ -- looks clunkier, but I find that it helps me remember that I have multivariate function.