can anybody solve partial deriavative
z=e^x^2 + xy with respect to x and y

Question

can anybody solve partial deriavative 
z=e^x^2 + xy with respect to x and y

yuki · Answer

yes

let's find f_x first

anonymous · Answer

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

yuki · Answer

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

anonymous · Answer

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

yuki · Answer

$$f_y = 0 + x = x$$

anonymous · Answer

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

yuki · Answer

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

yuki · Answer

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

anonymous · Answer

Try to find out yourself :)

anonymous · Answer

cool !!!

anonymous · Answer

lol that was fast :)

yuki · Answer

that was a lot easier than I thought lol

anonymous · Answer

Haha yeah

yuki · Answer

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 · Answer

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

anonymous · Answer

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

yuki · Answer

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 · Answer

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 · Answer

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