Question

How do you find the derivative of x^2 + y^2?

Answer 1

with respect to which variable?

Answer 2

like for economics we were given U(x,y) = x^2 + y^2 and were asked to find the margin utility with respect to x and y and we have to find partial derivatives but I don't know how to do it... :(

Answer 3

does that make sense at all??

Answer 4

yes, im trying to remember how to do those partial derivatives in general terms, lol
they didnt give you any specific points did they?

Answer 5

nope, all it says is U(x,y) = x^2 + y^2

Answer 6

like i have the answer, but i don't know how they got it... they said MUx = 2x and MUy = 2y

Answer 7

am i just over-thinking the question? lol

Answer 8

treat y as constant and differentiate then in second x as constant and then differentiate

Answer 9

Oh, okay, thats what I was going to say at first. I thought you were asking for something else.

basically, you take the derivative with respect to each variable separately.
so d/dx( x^2+y^2) the first goes to 2x (drop the power) the 2nd goes to 0 (no x var so it goes to 0) repeat for y.

Answer 10

i'm confused :(

Answer 11

what goes to 0?

Answer 12

the y^2 goes to 0, because there is no x value there. so, by definition of derivatives it will go to 0 when u derive it. Easy mode for derivatives (when you just have polynomials) is to drop the power. so x -> 1 and any constant -> 0

Answer 13

hmmm... so what is i had something like U(x,y) = (x)(y) + x?

Answer 14

if i ***

Answer 15

d/dx (x*y+x) = y+1
d/dy (x*y+x) = x

Answer 16

oh man i dont know why im finding this hard.... dont you have to do the product rule or something? or am i thinking of it too complicating?

Answer 17

No need for product rule, Like Ishaan said, just think of one or the other (x,y) as a constant, or just some number, and do your derivatives... if it's any consolation, lots of people have trouble with this.

Answer 18

hmmm i think i get it now hahaha... but just to make sure, what if i had something like this then: 3x + xy... would i get this: MUx = 3 + y and MUy = x ????

Answer 19

yes! exactly :)

Answer 20

woohoo!!!! thanks for your help, i have an assignment due tomorrow and its 2:30 am and i was desperate to get help.... at least now i dont feel completely dumb haha