anonymous
  • anonymous
can anybody solve partial deriavative z=e^x^2 + xy with respect to x and y
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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yuki
  • yuki
yes let's find f_x first
anonymous
  • anonymous
When you take the partial derivative with respect to x, consider y as a constant.
yuki
  • yuki
\[f = e^{x^2} + xy \] \[f_x = 2x*e^{x^2} + y\]

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More answers

anonymous
  • anonymous
\[{\partial z \over \partial x}=2xe^{x^2}+y\]
yuki
  • yuki
\[f_y = 0 + x = x\]
anonymous
  • anonymous
\[{\partial z \over \partial y}=x\]
yuki
  • yuki
Anwar you always surprise me. How did you get that "d" from ?!
yuki
  • yuki
Anwar you always surprise me. How did you get that "d" from ?!\[\partial\]
anonymous
  • anonymous
Try to find out yourself :)
anonymous
  • anonymous
cool !!!
anonymous
  • anonymous
lol that was fast :)
yuki
  • yuki
that was a lot easier than I thought lol
anonymous
  • anonymous
Haha yeah
yuki
  • 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
yuki
  • yuki
so it is actually not that hard. implicit differentiation is much more harder :)
anonymous
  • anonymous
it means u simply have to separate out the e^x ?
yuki
  • 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
yuki
  • 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
yuki
  • 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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