## INT 3 years ago find the partial derivatives with respect to x and y, if f(x,y) = $\sum_{n=0}^{}$ (xy)^n

1. INT

|xy| <1

2. Ahaanomegas

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

3. INT

(n)x^(n-1)? but what about the sum?

4. Ahaanomegas

@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.

5. INT

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

6. Ahaanomegas

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!

7. nitz

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

8. nitz

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

9. nitz

any query?

10. INT

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

11. nitz

ok first tell me the partial derivative of xy^3

12. nitz

wrt to x??????

13. nitz

just find out and tell me

14. INT

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

15. nitz

ya u find