anonymous
  • anonymous
Explain what derivatives are, and give a simple example of one
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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zzr0ck3r
  • zzr0ck3r
derivatives are slopes, at a point. y = 1 slope = 0 derivative of 1 = 0
anonymous
  • anonymous
A derivative is the infinitesimal rate of change at a certain point. For example in the equation y=x^2. The derivative is y' = 2x. Which means if we plug in x=1, 2(1)=2 which means the slope of the line y=x^2 at x=1 is 2.
zzr0ck3r
  • zzr0ck3r
hmm derivatives are not always infinitesimal, but what they call dx is.

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anonymous
  • anonymous
Is it the slope of anything, or just curves?
zzr0ck3r
  • zzr0ck3r
in 2d it is a slope of the curve given its differentiable there.
zzr0ck3r
  • zzr0ck3r
at that point.
zzr0ck3r
  • zzr0ck3r
note to talk about rate of change we need change in something / change in something if we are talking about a point then that change in something is 0 we cant divide by 0 so that change in something cant be 0 derivatives deal with taking care of that problem by considering very very very small change
anonymous
  • anonymous
Also the limit has to exist for the derivative to exist. For example at the changing point of an absolute value function there is no derivative because there is no slope at corners.
zzr0ck3r
  • zzr0ck3r
but this small change is not the derivative
anonymous
  • anonymous
can you tell me what must be learned before actually getting into the subject of derivatives?
zzr0ck3r
  • zzr0ck3r
nothing really, to understand it. But algebra before you can play with it
anonymous
  • anonymous
ok, thanks
zzr0ck3r
  • zzr0ck3r
how do we find slope?
anonymous
  • anonymous
of what?
zzr0ck3r
  • zzr0ck3r
rise/over run right?
anonymous
  • anonymous
of line is y1-y2/x1-x2
zzr0ck3r
  • zzr0ck3r
right
zzr0ck3r
  • zzr0ck3r
that is two points
zzr0ck3r
  • zzr0ck3r
now do the same thing with one point
zzr0ck3r
  • zzr0ck3r
x-x/y-y right?
anonymous
  • anonymous
In short derivative is the gradient. When speaking about functions the derivative describes the rate at which the variable x changes as variable y changes.
anonymous
  • anonymous
with 1 point, wouldnt it be y1/x1?
zzr0ck3r
  • zzr0ck3r
actually gradient points in the "fastest" derivative, they are not the same.
anonymous
  • anonymous
The gradient is none existent because you are talking about 1 point. There is no change
zzr0ck3r
  • zzr0ck3r
1 point, wouldnt it be y1/x1?
zzr0ck3r
  • zzr0ck3r
with one point we are finding the change in that point so we have y_1 - y_1/x_1 - x_1 = 0/0
zzr0ck3r
  • zzr0ck3r
calculus deals with that problem:)
anonymous
  • anonymous
As i have already mentioned above, the derivative is the rate of change. If you have 1 point there is no change.
anonymous
  • anonymous
oh thats what you meant, ok so its always 0/0, because there cannot be a change if another point isn;t involved, thats what i think
zzr0ck3r
  • zzr0ck3r
you most certainly can have a derivative at one point
anonymous
  • anonymous
|dw:1370038095851:dw|
zzr0ck3r
  • zzr0ck3r
^^^^ that thing is dealing with the divide by 0 problem
zzr0ck3r
  • zzr0ck3r
so go read a little about limits then watch a video on khan academy and you will have a great understanding of the derivative
anonymous
  • anonymous
Thank you zzr0ck3r, btw are you a teacher or student?
zzr0ck3r
  • zzr0ck3r
both
zzr0ck3r
  • zzr0ck3r
well I have to teach to graduate:)
anonymous
  • anonymous
lol, i am only in 9th grade :|
zzr0ck3r
  • zzr0ck3r
wow very cool.
zzr0ck3r
  • zzr0ck3r
I could not solve 3x = 6 in 9th grade:)
anonymous
  • anonymous
That is hard to believe >.>
anonymous
  • anonymous
You're in grad school?
anonymous
  • anonymous
@zzr0ck3r lol. You can have a derivative when you have a function, but if you just have 1 point, you do not have a derivative.
anonymous
  • anonymous
Not because it's an easy equation, but because you seem very smart
zzr0ck3r
  • zzr0ck3r
I c what your saying sorry
anonymous
  • anonymous
Are you at Harvard/MIT by chance? @tsolrm: You most certainly can have a derivative. We know what we are doing. Stop doubting us.
anonymous
  • anonymous
Future, are you at harvard or MIT?
zzr0ck3r
  • zzr0ck3r
I was just trying to get her to think about the dividing by 0 thing
zzr0ck3r
  • zzr0ck3r
or him
anonymous
  • anonymous
im a guy
anonymous
  • anonymous
@FutureMathProfessor Ah the idiot who thinks that division by zero gives infinity strikes again. Everyone hide!
zzr0ck3r
  • zzr0ck3r
um im not graduate, but I am in a program where we follow a teacher, then teach.
anonymous
  • anonymous
future, are you in harvard or MIT?
zzr0ck3r
  • zzr0ck3r
I doubt anyone doing this in their free time are idiots
anonymous
  • anonymous
I was going to say. If you were at MIT I would come over and say hi, but I guess not
zzr0ck3r
  • zzr0ck3r
ha im old and didn't graduate high school MIT would not have taken me.
anonymous
  • anonymous
@zzr0ck3r now that is where you are wrong. The smart guys hang out at stackexchange. This website on the other hand is aimed at helping kids with their homeworks.
anonymous
  • anonymous
what is stackexchange?
zzr0ck3r
  • zzr0ck3r
find me a happy man and one that hangs out at the stock exchange and tell me who is smarter
anonymous
  • anonymous
o stock exchange ok
zzr0ck3r
  • zzr0ck3r
im giving you pearls here, listen up
zzr0ck3r
  • zzr0ck3r
lol
anonymous
  • anonymous
ok im listening, what were you going to say?
zzr0ck3r
  • zzr0ck3r
not u
anonymous
  • anonymous
well, i gtg thanks for the help everyone
zzr0ck3r
  • zzr0ck3r
np
zzr0ck3r
  • zzr0ck3r
p.s @yoanjm1 kahnacademy!

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