Partial derivatives of level curves

[Calpalned]

Homework Statement

Let $C$ be a level curve of $f$ parametrized by t, so that C is given by $x=u(t)$ and $y = v(t)$
Let $w(t) = g(f(u(t), v(t)))$
Find the value of $\frac{dw}{dt}$

Homework Equations

Level curves
Level sets
Topographic maps

The Attempt at a Solution

Is it true that the answer to a level curve question is always zero? My teacher went over this but I couldn't understand him.

 

[Brian T]

What does it mean to be on a level curve? What value will f put out for any changes in t? How does the g or w function change corresponding to f's change.