# 3D Differentiation

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#1
Hi, I'm trying to solve a statistical probability problem where the P of an event is based on two variables, x and y such that:

P = x/(x+y) + (50-x)/(100-x-y)

I want to find the values of x and y that give the max P:

or where dP/d(x,y) = 0

How do I do this calculation?

Thanks for any help - much appreciated.
0
16 years ago
#2
I know it's an incredibly messy method but from all I know I'd try and get an equation in x or y and substitute...
0
16 years ago
#3
(Original post by ZJuwelH)
I know it's an incredibly messy method but from all I know I'd try and get an equation in x or y and substitute...
3D Differentiation?

Right........
0
16 years ago
#4
As you can tell my knowledge of calculus does not extend to dealing with a third variable. But I can do parametric and implicit differentiation...

I've just had an idea, why not do implicit differentiation?
0
16 years ago
#5
you have to solve partial dP/dx = 0 and partial dP/dy = 0 simultaneously. (and then do some other stuff to find out if it's a maximum, minimum or saddle point)
0
16 years ago
#6
like the post above, search on google for the topic of partial differentiation. You will hopefully find all your answers there.

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