Question

find the partial derivatives with respect to x and y, if f(x,y) = \[\sum_{n=0}^{}\] (xy)^n

Answer 1

|xy| <1

Answer 2

So, wrt to one variable, you treat the other as a constant. So how would you differentiate (constant*x)^n?

Answer 3

(n)x^(n-1)?

but what about the sum?

Answer 4

@First question - Yep.
@Second question - What's the upper limit? Also, what's the |xy| < 1 for?

Sorry, I'm not quite understanding the question fully.

Answer 5

the upper limit is infinity.
|xy|<1 is the condition that goes along with the question

Answer 6

Ah! Makes sense. So, basically, for x, it would be: \[ \displaystyle\sum_{n=0}^{\infty} nx^{n-1}. \]At this point, I'll just wait for another response. I really have no idea myself. Sorry. :( All the best!

Answer 7

patial derivative wrt to x
\[\sum_{n=0}^{n=\infty}nx ^{n-1}y ^{n}\]

Answer 8

and wrt to y
\[\sum_{n=0}^{n=\infty}x ^{n}(ny ^{n-1})\]

Answer 9

any query?

Answer 10

I dont think that is quite right.

I dont get how you take a partial of a sum and how you would account for |xy| < 1

Answer 11

ok first tell me the partial derivative of xy^3

Answer 12

wrt to x??????

Answer 13

just find out and tell me

Answer 14

find 2 different partials,
one with relation to x and one with relation to y

Answer 15

ya u find