Chapter 1, Problem 1.28E

For the following function, evaluate the derivatives in a-f below.

${\text{F(w,x,y,z) = 3xy}}^2+\frac{w^3{z}^3}{32y}-\frac{x{y}^2{z}^3}{w}$

$\begin{array}{l}a.{\left(\frac{\delta F}{\delta x}\right)}_{w.y,z}\\ b.{\left(\frac{\delta F}{\delta w}\right)}_{x,y,z}\\ c.{\left(\frac{\delta F}{\delta y}\right)}_{w.x,z}\\ d.\left[\frac{\delta }{\delta z}{\left(\frac{\delta F}{\delta w}\right)}_{w.y,z}\right]{}_{w,y,z}\\ e.\left[\frac{\delta }{\delta z}{\left(\frac{\delta F}{\delta w}\right)}_{w.x,y}\right]{}_{w,y,z}\\ f.{\left\{\left[\frac{\delta }{\delta z}{\left(\frac{\delta F}{\delta w}\right)}_{w.x,y}\right]{}_{w,y,z}\right\}}_{x,y,z}\end{array}$