1. ## Partial derivatives

I'm trying to revise but I can't seem to solve this:

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???

2. Note, for some reason the file only opens if you click on the empty space twice

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

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

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

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

From here just sub in