Question

Partial Differentiation Problem:
Determine fx when
f(x, y) =
(2x + y)/
(x + 2y)

@agent0smith

Answer 1

Is:
\[f(x)=\frac{2x+y}{x+2y}\]

Answer 2

yes @KeithAfasCalcLover

Answer 3

just use the quotient rule

Answer 4

So you would have:
\[\frac{\partial}{\partial x}\frac{2x+y}{x+2y}=\frac{\partial}{\partial x}\frac{f(x,y)}{g(x,y)}\]
So we can obtain:
\[\frac{\partial}{\partial x}\frac{f(x,y)}{g(x,y)}=\frac{f_x(x,y)g(x,y)-g_x(x,y)f(x,y)}{g(x,y)^2}\]

Answer 5

Clear so far?

Answer 6

you probably shouldn't use f(x,y) in your explanation since it is already defined to be the entire original problem.

Answer 7

Fair point. But I was just stating in general that for any \(\frac{f(x,y)}{g(x,y)}\), that would be the derivative

Answer 8

I know...just wanted to avoid confusion for the OP

Answer 9

What is OP?

Answer 10

original post (or poster)

Answer 11

Will avoid that next time. Good Point!

Answer 12

hopefully pancakeslover can add something here since he/she now has a formula

Answer 13

I agree! I like to give a general solution first. But I must go haha so I will talk to you later!

Good Night everybody!

Answer 14

no i got it!! thank you! I just have to keep y as a constant and differentiate with respect to x. Thank you!