Good afternoon,
I have a function with multiple inputs one of which is a function, for example: $T(u,w,y,v(x),z)$
Now $v(x)$ is a function of multiple inputs (parameters to a model): $v(x) = G(p_1,p_2,p_3,...,p_n)$
As I change $ p_3$ value from h to $h+1$, I can see the impact the parameter has on $T(x)$, graphically. I seek to find the maximum of this impact curve and then optimise $v(x)$ by changing the value of another parameter,$ p_1$ such that the maximum $p_3$ impact occurs at a fixed point K. Changing the other parameters of v(x) changes the $p_3$ max impact magnitude and point K. This is okay, as I can recalibrate and reset $p_1$ value.
How do I differentiate $T(x)$ wrt $p_3$?
I imagine I can set this differential equation to $0$, to find a maximum, then run a Solver to optimise the value of p1, such that the differential $= 0.$
Sorry for math notation above not being optimal, first post.
Cheers, Anthony
If I understand correctly, $x = (p_1,p_2,p_3,\dots,p_n)$. Apply simply the chain rule to $T(w,p_1,p_2,p_3,\dots,p_n,y,v(p_1,p_2,p_3,\dots,p_n),z)$.