## anonymous 5 years ago can anybody solve partial deriavative z=e^x^2 + xy with respect to x and y

1. Yuki

yes let's find f_x first

2. anonymous

When you take the partial derivative with respect to x, consider y as a constant.

3. Yuki

$f = e^{x^2} + xy$ $f_x = 2x*e^{x^2} + y$

4. anonymous

${\partial z \over \partial x}=2xe^{x^2}+y$

5. Yuki

$f_y = 0 + x = x$

6. anonymous

${\partial z \over \partial y}=x$

7. Yuki

Anwar you always surprise me. How did you get that "d" from ?!

8. Yuki

Anwar you always surprise me. How did you get that "d" from ?!$\partial$

9. anonymous

Try to find out yourself :)

10. anonymous

cool !!!

11. anonymous

lol that was fast :)

12. Yuki

that was a lot easier than I thought lol

13. anonymous

Haha yeah

14. Yuki

anyway, zizUo, with partial derivatives you will treat the other variable as same as numbers, so for f_y, the term $e^{x^2}$ has no y in it, so it's derivative is 0 since you treat is as if it's a number

15. Yuki

so it is actually not that hard. implicit differentiation is much more harder :)

16. anonymous

it means u simply have to separate out the e^x ?

17. Yuki

e^x^2 has no y in it, so the partial derivative of e^x^2 with respect to y, is as same as taking the derivative of a number like 10 or 34

18. Yuki

on the other hand, the term xy has a y multiplied to x, so it is similar to saying " find the derivative of 2y" which is 2 in our case, x is the constant, so the partial derivative of xy is x

19. Yuki

on the other hand, the term xy has a y multiplied to x, so it is similar to saying " find the derivative of 2y" which is 2 in our case, x is the constant, so the partial derivative of xy is x

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