Question

Let f(x,y) = (−(4x+y))5. Then

[(∂2f)/(∂x∂y)] = ???
[(∂3f)/(∂x∂y∂x)] = ???
[(∂3f)/(∂x2∂y)] = ???

Answer 1

\[f=(-(4x+y))^5?\]

Answer 2

yes

Answer 3

\[f=-(4x+y)^5 \]
\[f_x=-5(4x+y)^{5-1}(4)=-20(4x+y)^4\]

Answer 4

\[f_{xy}=-20 \cdot 4(4x+y)^{4-1}(1)=-80(4x+y)^3\]

Answer 5

all you have to do is treat everything else like a constant except the one you are differentiating with respect to

Answer 6

\[f_{xyx}=-80(3)(4x+y)^{3-1}(4)\]

Answer 7

you should try the last one

Answer 8

i will be happy to check it

Answer 9

why multiply that last one by 4 ?!

Answer 10

chain rule

Answer 11

so -900(4x+y)^2 ?

Answer 12

partial derivative with respect to x of 4x+y is 4
parital derivative with respect to y of 4x+y is 1

Answer 13

i know that ! but my question is how is that thing works !? [(∂^3f)/(∂x∂y∂x)]

Answer 14

?

Answer 15

i know its higher order but the signs for it are hella confusing

Answer 16

so in the last one i do it considering x twice then with y one !?

Answer 17

yep

Answer 18

i already did f_x
now you have to find f_xx
then f_xxy

Answer 19

ok cool thanks

Answer 20

i like this notation more than the one above
it looks less messy i think lol