Question

find the 1st and 2nd order of partial derivatives of f(x,y,z)= x^2yz^4e^z(y)^4

Answer 1

The format confuses me, is this what you mean?
\[f(x,y,z)=x^2yz^4e^zy^4\]

Answer 2

yes sorry, except at the end the z and y are to the power of e and y is to the power of 4

Answer 3

So, this:
\[f(x,y,z)=x^2yz^4e^{zy^4}\]With respect to which variables, all three?

Answer 4

yes all three

Answer 5

treat everything else like a constant except the thing you are taking partial derivative with respect to

Answer 6

i was looking at the first equation

Answer 7

so we should be looking at the second equation right?

Answer 8

yay partial derivatives are easy

Answer 9

\[f_x=2x*yz^4e^{zy^4}\]

Answer 10

yes that's the equation

Answer 11

Sorry it's x^2 and everything else

Answer 12

do you want to try f_z on your own

Answer 13

cmon do it with respect to z

Answer 14

\[f_y=x^2(1)z^4e^{zy^4}+x^2yz^4(4zy^3)e^{zy^4}\]

Answer 15

those z's look funny to me

Answer 16

\[∂f/∂x=2xyz^4e^{zy^4}\]\[∂f/∂y=x^2z^4e^{zy^4}(4zy^4+1)\]\[∂f/∂z=x^2yz^3e^{zy^4}(zy^4+4)\]

Answer 17

what about the second order of them?

Answer 18

Does someone know how to do the second order?

Answer 19

just do the same way we have been doing

Answer 20

if you are taking derivative with respect to x then treat everything else like a constant except x

Answer 21

ok, thank you all