Partial derivatives of level curves

1. Mar 1, 2015

Calpalned

1. The problem statement, all variables and given/known data
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 $\frac{dw}{dt}$

2. Relevant equations
Level curves
Level sets
Topographic maps

3. 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.

2. Mar 1, 2015

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.