Question

Find the differential dy.
x^2 + y^2 = 25

Answer 1

So a differential is basically the same procedure as taking a derivative,
It's just that uhhhhh.. Mmm I can't think of a good way to describe it -_-

Derivative of the first term is 2x, yes?
Applying the chain rule gives us a dx attached to it.

Same idea with the y's.\[\Large\rm 2x~dx + 2y~dy = 0\]And derivative of a constant is zero.
Understand how to solve for dy from that point?

Answer 2

2y dy = -2x dx ?

Answer 3

Mmm k :o
then just finish it up with some division yes?

Answer 4

dy = - x dx / y ?

Answer 5

Yay good job \c:/

Answer 6

that's the final answer?

Answer 7

Yah looks good.
if we had written it as a normal derivative we would have:
dy/dx = -x/y

You can see the only different here is that the differentials are separated.

Answer 8

ahh. okay. got it. :) thanks. ^__^