# Hard Partial Derivatives question

1. Oct 24, 2012

### steve0606

1. The problem statement, all variables and given/known data
Taking k and ω to be constant, ∂z/∂θ and ∂z/∂ф in terms of x and t for the following function
z = cos(kx-ωt), where θ=t2-x and ф = x2+t.

2. Relevant equations

3. The attempt at a solution
I'm finding this difficult as t and x are not stated explicitly. I know how to do the chain rule with partial differentiation.

2. Oct 24, 2012

### HallsofIvy

Staff Emeritus
Then where did you get this problem? The chain rule for more than one variable is given in any Calculus text.

$$\frac{\partial f}{\partial \theta}= \frac{\partial f}{\partial x}\frac{\partial x}{\partial \theta}+ \frac{\partial f}{\partial t}\frac{\partial t}{\partial \theta}$$

$$\frac{\partial f}{\partial \phi}= \frac{\partial f}{\partial x}\frac{\partial x}{\partial \phi}+ \frac{\partial f}{\partial t}\frac{\partial t}{\partial \phi}$$