Consider a radial function z=g(r). Let P be the point with polar coordinates $\displaystyle (r,\theta)=(2,\frac{\pi}{3})$ and suppose g'(2)=3

Evaluate: $\displaystyle \frac{\partial z}{\partial x}$ at P if y is held constant.

I know that give a function z=f(x,y) z can be determined given f and any two of x, y, r, $\displaystyle \theta$

I attempted to make a tree diagram for this problem.