Derivative of $F$ with respect to $W$

Question

Let $g$ be the derivative of a function $F$ with respect to $Z$ where $Z = WX$

(i.e. $\frac{\partial}{\partial Z}F = g$ where $Z = WX$ )

If I want to find the derivative of $F$ with respect to $W$. How do I find that?

(i.e. What is the value for $\frac{\partial}{\partial W}F$ ?)

Note: I know chain rule is involved somehow but I don't know how exactly is it involved

Answer 1

Well, instead of the answer, you can try understading the theory. Here's a screenshot from Thomas' Calculus (13th ed) which might help you...

And another one:

If you can, read the explanation from the book as well. Try your question again.

Answer 2

Logarithmic differentiation and Chain rule

$$ Z=WX, \; \log Z = \log W+\log X$$

$$ \dfrac{\frac{\partial Z}{\partial W}}{Z} = \dfrac{1}{W} + \dfrac{\frac{\partial X}{\partial W}}{X} $$

Again plug in $$Z=WX.$$