Question

find partial derivative of f(x,y,z) = xyln(z^2 + xy) with respect to z.

Answer 1

You are to treat everything but z as a constant when taking the partial w.r.t z

Answer 2

So for example do you know how find the derivative of G(z)=2(3)ln(z^2+2(3))
?

Answer 3

You would use constant multiple rule for the 2(3) part...
Chain rule for the ln(z^2+2(3)) part
and power rule for the z^2 part

Answer 4

I'm not saying replace x and y with 2 and 3. I'm just saying treat them as you would 2 and 3 or some other constant.

Answer 5

I think my confusion has to do with just taking derivatives of lnx/log(x)

Answer 6

So the derivative of the inside function with respect to z would just be 2z correct?

Answer 7

\[\frac{ d}{dz}\ln(f(z))=\frac{f'(z)}{f(z)}\]

Answer 8

yeah

Answer 9

Because if you treat x*y as a constant, the derivative of a constant is just 0.

Answer 10

correct

Answer 11

So 2z/(xyln(z^2 + xy) ?

Answer 12

the only trouble i have with your answer is the (xy) factor on bottom

Answer 13

I don't like that is it on bottom

Answer 14

\[\frac{\partial f}{\partial z}=xy \cdot \frac{2z}{z^2+xy}\]

Answer 15

the xy in front was just a constant multiple
just bring it down

Answer 16

oh and i didn't notice you left the ln intact

Answer 17

that is another problem

Answer 18

\[\frac{ d}{dz}\ln(f(z))=\frac{f'(z)}{f(z)} \]
no ln in the derivative here

Answer 19

just differentiating the inside and putting it over the inside

Answer 20

Oh alright. So basically it's just a matter of using the chain rule and knowing the derivative of lnx = 1/x ?

Answer 21

yes

Answer 22

i would stay longer and give you some problems to try but i must go now

Answer 23

No problem, thanks!