Question

p

Answer 1

you want\[\nabla z\over\nabla x\]and\[\nabla z\over\nabla y\]?

Answer 2

if you show me just one of those partial derivatives i'll know how to find the other

Answer 3

do I understand the problem correctly?

Answer 4

I don't think I do since it seems to make no sense to me...

Answer 5

the partial derivative of z with repsect to x. del z/ del x or die z / die x . that symbol that is used for partial derivatives that looks like a two kind of

Answer 6

ooooh I see, but you are not given any more info besides
x=f(xy) ?

Answer 7

z=f(xy)

Answer 8

yeah. that's it.

Answer 9

well then I suppose all there is to do is apply the chain rule...

Answer 10

so i can start off by going z - f(xy) = 0 then i need to find the partial derivative of x, so f_x then f_y and f_z and del z/ del x = -f_x / f_z

Answer 11

do i let xy =z then use the chain rule?

Answer 12

okay I am confused again,\[z=f(xy)\]as in "z equals a function of x times y" correct?

Answer 13

actually no, i know how to do these when there are actual numbers but i'm not quite sure with the f(xy)

Answer 14

yeah

Answer 15

oh wait I invented a z, sorry

Answer 16

okay but this is a multiple choice question and my options are like f'(x)f(y) or xf '(xy) ect...

Answer 17

okay let me rethink this for a sec...

Answer 18

oh I see

Answer 19

i know what i want to do but i'm not quite sure how to do it. the only thing throwing me off is f(xy) so if i take the partial derivative of that with respect to x, i hold y constant. if it was a normal expression no problem but since its not i'm a little confused

Answer 20

would it be f ' (x) f(y) ?

Answer 21

my reasoning gives\[\frac{\partial }{\partial x}z=\frac{\partial }{\partial x}f(xy)=\frac{\partial f}{\partial x}\cdot\frac{\partial }{\partial x}(xy)=y\frac{\partial f}{\partial x}=yf_x(xy)\]but the choices in your answer are for f' (whole derivatives on f, not partial)???

Answer 22

that's correct.

Answer 23

correct as in they're not partial derivatives for my choices of answers

Answer 24

so I guess then they want\[\frac{\partial }{\partial x}z=\frac{\partial }{\partial x}(xy)f'(xy)=yf'(xy)\]

Answer 25

this would make sense, you can check it with a function like z=sin(xy), z=(xy)^2, whatever

Answer 26

okay thanks!

Answer 27

welcome!

Answer 28

if the question's asking for partial derivatives then z = f(x*y) makes sense.

If the question's asking for the total differential wrt x or y than they could just be asking about the chain rule and z= f(x, y)