Question

Help with differentials.

Answer 1

In this question, I'm asked to find the differentials of each term, how do I do this? \[y^3 - xt - 1 = x^2 + y^2\]

Answer 2

@Directrix

Answer 3

help still tengo

Answer 4

Español

Answer 5

@zepdrix

Answer 6

1sec i think i did this before

Answer 7

if you Note that if we are just given then the differentials are df and dx and we compute them in the same manner.

you are also Given a function we call dy and dx differentials and the relationship between them is given by,

Answer 8

There's a function here?

Answer 9

what

Answer 10

" you are also Given a function"

Answer 11

ok what u think function is

Answer 12

Something that isn't in this equation....?

Answer 13

the medal ?

Answer 14

is it fixed medal accdeint

Answer 15

I don't know what you're talking about.

Answer 16

im trying to guess what function that has nothing to do with equation u are talking about so i thought was the medal so can u EXPLAIN WHAT UR TALKING ABOUT ?

Answer 17

\[y^3 - xt - 1 = x^2 + y^2\]
take differential through out
\[3y^2dy - (dx*t+x*dt) = 2xdx+2ydy\]

grouping terms we get
\[dy(3y^2-2y) + (-t-2x)dx -xdt=0\]

Answer 18

\[y^3 - xt - 1 = x^2 + y^2\]
take differential through out
\[3y^2dy - (dx*t+x*dt) = 2xdx+2ydy\]

grouping terms we get
\[(3y^2-2y)dy + (-t-2x)dx -xdt=0\]

Answer 19

makes sense i get it

Answer 20

So about the term \[y^3\], why does it become \[3y^2 dy\] ?

Answer 21

whats the derivative of \(u^3\) with respect to \(u\) ?

Answer 22

3u du? "with respect to u," what does it mean?

Answer 23

I suggest you watch this video
http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/2.-partial-derivatives/part-b-chain-rule-gradient-and-directional-derivatives/session-32-total-differentials-and-the-chain-rule/

Answer 24

Oh wait. Lemme think. So if I take the differentials of this equation: \[y^2 - xy = \sin x\]
I'll end up with \[2 ydy - xdy - ydx = cosx dx\]

Answer 25

Yes that looks good! but still could you please watch that video, that video explains differentials a bit more accurately...

Answer 26

Whew. I'm terrible with differentials. x_x Thanks! I will!

Answer 27

I'm sure that video clears up everything! yw :)