Question

What does it mean to just have dy by itself, instead of dy/dx

Answer 1

change in y pretty much

Answer 2

dy is the differential of the function y..

Answer 3

\[m = \frac {\Delta y}{\Delta x} = \frac {dy}{dx}\]

Answer 4

well Rogue, dy is often used for approximation of the functions because of the reason it's very near by delta y but not so close to use the equal sign....careful with that...:D

Answer 5

for example you wish to know how much volume of the sphere with radius 15 m changes if the radius is increased by 2mm....you can calculate two volumes, and then take delta V (delta y in your case)....the faster but not 100 percent accurate is to calculate the differential: dV=(dV/dR)*dR and you'll get change in volume approximatelly as delta V...but the ''small mistake'' is always there...that's when you can use differentials of higher order to reduce that mistake, I think that quadratic approximation or d(dy) is accurate enough....:D

Answer 6

Ah, ok, I assumed differentials and deltas were pretty much the same thing since I just skimmed that section in my textbook.
My calc. teacher glanced over DE by just doing seperable DE's with us. We'll do actual DE's after the ap exam. I hope they're not too hard =)

Answer 7

well, when the change in x is small, in real life you can tell that they are equal, that's way it's made :D:D ...