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