- Problem Statement
- see post
- Relevant Equations
- dz/dr = dz/dx (dx/dr) + dz/dy(dy/dr)
It seems that the way to combine the information given is
z = f ( g ( (3r^3 - s^2), (re^s) ) )
we know that the multi-variable chain rule is
(dz/dr) = (dz/dx)* dx/dr + (dz/dy)*dy/dr
(dz/ds) = (dz/dx)* dx/ds + (dz/dy)*dy/ds
---(Parentheses indicate partial derivative)
other perhaps useful information
I don't know how to apply this information because, usually, there is only one variable, like t, being fed into the multi-input function, and the chain rule works nicely. But here we have r and s being fed into the multi-input function g. Further, g is the input of the function f, which is z. In order to obtain the derivative of z with respect to g, we would need to know the function f(g). It is not given. I would guess that the way to find the derivative of z with respect to r would be to multiply the derivative of z with respect to g by the derivative of g with respect to x, multiplied by the derivative of x with respect to r, plus the derivative of z with respect to g multiplied by the derivative of g with respect to y, multiplied by the derivative of y with respect to r.
So that is where I am on this. Thanks for any assistance.