Question

partial derivatives...

Answer 1

show that \[ \frac{∂^{ 2} z }{ ∂x ∂y } = \frac{ ∂^2 z }{ ∂y∂x }\]

1. z = x+y/x-y
2. \[z= (x^2 + y^2)^\frac{ 3 }{ 2}\]

Answer 2

that's 3/2

Answer 3

http://www.wolframalpha.com/input/?i=D [D[%28x%2By%29%2F%28x-y%29%2C+x]%2Cy]

Answer 4

http://www.wolframalpha.com/input/?i=D [D[%28x%2By%29%2F%28x-y%29%2C+y]%2Cx]

Answer 5

http://tinyurl.com/8h8xop3

Answer 6

differentiate it usually as you do keeping the other variable as constant.

Answer 7

first do the partial derivative for x and then y, then do the partial derivative all over again but now start with y then do the partial for x

your answers should both equal each other, no matter which way you had approached it

Answer 8

thank you so much! :))

Answer 9

your most welcome

Answer 10

is it equal to \[\frac{ -4xy}{ (x-y)^{4}}\] ??

Answer 11

I really did not try it, but try it both ways and see, you have to get the same answer in both methods, I will try it in a few minutes.

Answer 12

http://www.wolframalpha.com/input/?i=D [D[%28x^2%2By^2%29^%283%2F2%29%2C+y]%2Cx]+

Answer 13

yeah the second partial derivative is pretty difficult, I got a different answer to your answer.
let me try the other way

Answer 14

no...that one is the result when

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