Question

how do i find f_xy of f(x,y)=x^3+y^3-xy

Answer 1

first find f_x

Answer 2

To do that pretend y is a constant

Answer 3

ive found it and f_y. i cant seem to understand the f_xy concept though.

Answer 4

\[(f_x)_y=f_{xy}\]

Answer 5

you find f_x
then you find the partial of that w.r.t y

Answer 6

for example
\[f(x,y)=e^{3x+2y} \\ f_x=(3+0)e^{3x+2y} =3e^{3x+2y} \\ f_{xy}=(f_x)_y=(3e^{3x+2y})_y=3(0+2)e^{3x+2y}=6e^{3x+2y}\]

Answer 7

so first what did you get for f_x

Answer 8

i got that f_x = 3x^2-y

Answer 9

\[f=x^3+y^3-xy \\ f_x=3x^2-y \\ f_{xy}=(f_x)_y=(3x^2-y)_y\]

Answer 10

now you find the partial of what you just found w.r.t. to y

Answer 11

\[(3x^2)_y-(y)_y=?\]

Answer 12

i think its -1

Answer 13

yep

Answer 14

Awesome! thank you so much!

Answer 15

np