Hard Partial Derivatives question

[steve0606]

Homework Statement

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.

Homework Equations

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.

 

[HallsofIvy]

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

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

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