# Partial derivatives

• May 9th 2009, 09:23 AM
Roland25
Partial derivatives
I'm trying to revise but I can't seem to solve this:

Attachment 11329

The problem is that for 4 marks it's taken me way too long to expand and differentiate.

Is there a shortcut that I'm missing???
• May 9th 2009, 09:29 AM
Roland25
Note, for some reason the file only opens if you click on the empty space twice
• May 9th 2009, 09:31 AM
TheEmptySet
Quote:

Originally Posted by Roland25
I'm trying to revise but I can't seem to solve this:

Attachment 11329

The problem is that for 4 marks it's taken me way too long to expand and differentiate.

Is there a shortcut that I'm missing???

Use the chain rule

$\displaystyle \frac{\partial f}{\partial u} = \frac{\partial f}{\partial x}\frac{\partial x}{\partial u}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial u}+\frac{\partial f}{\partial z}\frac{\partial z}{\partial u}$

$\displaystyle \frac{\partial f}{\partial u}=(3x^2-2xy)(1)+(-x^2-2z^2y)(1)+(-2zy^2)(0)$

From here just sub in