Question

Hi everyone! Can someone discuss with me the purpose of a "total differential" and what it really represents? Thanks! :o)

Answer 1

what do you think it is.

Answer 2

well...the derivative of a function is the rate of change or the slope of that function at a given point y with respect to x...i get that part...

so like if I have an equation y=x^2 + 2 the derivative is simply 2x...but what confuses me is that when you get an equation like f(x,y)=x^2y^2...if I take the derivative with respect to x, it's a bit confusing because there is a "y" in the function whereas in the first equation there is only an x to deal with...can you help me understand what I am finding the slope of? Is it a 3rd dimension or something?

Answer 3

ok that messed up hold on

Answer 4

omg...in your answer i see a bunch of black diamonds with question marks inside them...i don't think i am displaying what you wrote correctly

Answer 5

http://en.wikipedia.org/wiki/Differential_of_a_function#Differentials_in_several_variables

Answer 6

try that sorry

Answer 7

try what? the wiki link?

Answer 8

yes

Answer 9

yeah that doesn't help, sorry...i need to discuss it, not read all the mathese...i appreciate the help but I could have looked that up on my own, which I did earlier...can you just try and explain it to me?

Answer 10

was i correct about the total differential being the slope of both x and y in the 3rd dimension(z axis)?

Answer 11

yes

Answer 12

you know the mean part

Answer 13

do you know df dimensions

Answer 14

actually...

Answer 15

my next question was if you could help me figure out the mechanics of solving a total differential...for example:
given f(x,y)=x^2y^2
can you show me mechanically why the answer is df = 2xy^2 dx + 2x^2y dy
I can't figure out how they get the dx and dy and df in their places

Answer 16

@Kainui @jim_thompson5910

Answer 17

I have looked at youtube but I can't seem to find a good video...can anyone refer me to a good video that explains the dx dy df thingy?

Answer 18

try this
http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-11-chain-rule/

Answer 19

Thanks Ganeshie...I will look right now

Answer 20

quick question Ganeishi...

Answer 21

so the video just simply says that the differential of f(x,y)=df as far as the left side of the equation goes...

typically when you take the derivative of say f(x), you would write:
d(f)/dx...since you are taking the total derivative of say f(x,y),
is "df" like writing d(f)/dxdy or something like that? I am trying to understand where the "df" comes from mechanically

Answer 22

d(f)/dxdy doesn't really make sense though because you would because it would look like df= stuff dxdy + morestuff dxdy rather than
df=stuff dx + morestuff dy...can anyone explain what I am missing?

Answer 23

or did I not watch enough of the video :o~ ?

Answer 24

okay...I think I understand. "df" is not a number, so I can't expect to manipulate d(f(x,y)) like you normally would..."df" is "equal" to the "idea" of combining d(f)/dx +d(f)/dy +d(f)/dz = df :o) right?

Answer 25

thanks!