Question

what is partial derivative of f(x,y,z,t)=xyz^2tan(yt) what is partial derivative of f(x,y,z,t)=xyz^2tan(yt) @Mathematics

Answer 1

which partial you want? x,y,z, or t?

Answer 2

i dunno, you got a funky looking exponent in there that scares me

Answer 3

its a product so i see a product rule in the future

Answer 4

but maybe not since the non variables get treated as constant

Answer 5

F(x,y,z,t)=xyz^2tan(yt)

Fx = yz^(2tan(ty))

that is all exponent right?

Answer 6

with respect to eachj variable jus the z is squared

Answer 7

\[F(x,y,z,t)=x\ y\ z^2\ tan(yt)\]
thats easier then, i hope

Answer 8

yes the (yt) is what gets me

Answer 9

Fx = y z^2 tan(yt)

Fy = [Cy*tan(yC)]' = C'y*tan(yC)+Cy*tan'(yC)

= xz^2 tan(yt) + xyz^2* t sec^2(yt)

Fz = 2xyz tan(yt)

so far

Answer 10

it is with respect to y or with respect to t that complex

Answer 11

Fy means with respect to y

Ft might be cleaner tho

Answer 12

thank you i see its the product rule now

Answer 13

Ft = [C tan(Ct)]' = C*Csec^2(Ct)

= xyz^2 *y sec^2(yt)

Answer 14

might wanna use different terms for the different constant blocks, but thats the gist of it

Answer 15

Ft can go to: x y^2 z^2 sec^2(yt)

Answer 16

r u a teacher/tutor?

Answer 17

nope, just a person who is trying to remember what i learned about it along time ago :)

Answer 18

im taking calc3 diffy qs and linear algebra next semester tho

Answer 19

lol what? retaking them right?

Answer 20

if i ever have to "retake" a math course, just shoot me ;)

nah, im finally going to college to get a degree. Most of this stuff i taught meself.

Answer 21

well, most of this stuff i taught myself from reading books ... i wish i could have just invented it lol