Partial derivatives

**Roland25** · May 9th 2009, 09:23 AM

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

$Partial derivatives-eq.latex.gif$

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???

**Roland25** · May 9th 2009, 09:29 AM

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

**TheEmptySet** · May 9th 2009, 09:31 AM

Originally Posted by Roland25

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

$Click image for larger version. Name: eq.latex.gif Views: 18 Size: 4.4 KB ID: 11329$

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

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

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

From here just sub in

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