Chapter 14.5, Problem 4PT

Find $\frac{\partial z}{\partial x}$ for $z=f\left(x,y\right)$ defined implicity by $\frac{x^2}{4}-\frac{y^2}{9}+\frac{z^2}{16}=0$.

1. a) $\frac{-x}{4z}$
2. b) $\frac{x}{4z}$
3. c) $\frac{-4x}{z}$
4. d) $\frac{4x}{z}$