(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that u(x,y) and y(x,z) are both continuous, differentiable functions show that

([itex]\frac{\partial u}{\partial z}[/itex])_{x}=([itex]\frac{\partial u}{\partial y}[/itex])_{x}([itex]\frac{\partial y}{\partial z}[/itex])_{x}

2. Relevant equations

Only equations given above

3. The attempt at a solution

I tried to write out the total differential for du and dy and then holding x constant so dx=0 I rearranged the equations to get

[itex]\frac{du}{dz}[/itex]=([itex]\frac{\partial u}{\partial y}[/itex])_{x}([itex]\frac{\partial y}{\partial z}[/itex])_{x}

I then tried to get [itex]\frac{du}{dz}[/itex] in another form but couldn't see a way of getting ([itex]\frac{\partial u}{\partial z}[/itex])_{x}from what I have.

Any help would be greatly appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Manipulation of partial differential operators.

**Physics Forums | Science Articles, Homework Help, Discussion**