Question

\[\text {Find the partial derivatives with respect to z, x, and y.}\]
\[2x^2 + 4xy + z^2 = 25\]
@Luigi0210 enjoy.

Answer 1

So:
\[\LARGE f_{z}:3z^2=0\]?

Answer 2

Find dz/dx with respect to x, treat y as a constant.

Answer 3

that has nothin to do with dis problem

Answer 4

basically you differentiate implicitly

Answer 5

Sorry, my head's still in the gutter

Answer 6

Hmm, I think I looked at the wrong video then ._.

Answer 7

Teach me step-by-step sham.

Answer 8

\[2x^2 + 4xy + x^2 = 25\]
dz/dx with respect to x.
treat y as a constant.
\[4x + 4y + 2zz' = 0\]
\[z'(2z) = -4(x+y)\]
\[z' = \frac{ -2(x+y) }{ z }\]

Answer 9

make sense?

Answer 10

you don't use the product rule for 4xy because we are treating y as a constant :P

Answer 11

Other than that x^2 in the beginning that's suppose to be a z.. I follow xD

Answer 12

huh?

Answer 13

well anyways, i know you can do implicit diff
try it for dy/dx

Answer 14

remember
dy/dx means with respect to x. so this time z is a constant :)
and the derivative of a constant is zero.

Answer 15

\[\LARGE 2x^2 + 4xy + z^2 = 25\]
\[\LARGE 4x+4y'+z^2=0\]
Am I right so far..? Probably not..

Answer 16

nope, you treat z as a constant

Answer 17

\[4x + 4y + 4xy' = 0 \]
and you forgot the product rule too

Answer 18

Ugh, I'm not focused enough..

Answer 19

\[y' = \frac{ -(x+y) }{ x }\]

Answer 20

What notes/websites did you use to learn this stuff?

Answer 21

not much really.
i used my calc book mostly.
i looked at this tho http://tutorial.math.lamar.edu/Classes/CalcIII/PartialDerivatives.aspx

Answer 22

What's the name of dat calc book of yours anyways? xD

Answer 23

oh and the notation for y' is
\[f_y (x,y,z) = \frac{ -(x+y) }{ x }\]
\[f_z (x,y,z) = \frac{ -2(x+y) }{ z }\]

Answer 24

and z*

Answer 25

i'm using thomas transcendental 10th edition
and james stewart 5e i think

Answer 26

Alrighty, let me get more familiar with the topics and such and I'll get back to y'all on it~

Answer 27

http://www.amazon.com/Calculus-5th-James-Stewart/dp/053439339X/ref=sr_1_4?s=books&ie=UTF8&qid=1388128451&sr=1-4&keywords=calculus+james+stewart
that one

Answer 28

do the last one!
d/dx