Explain what derivatives are, and give a simple example of one

- anonymous

Explain what derivatives are, and give a simple example of one

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- zzr0ck3r

derivatives are slopes, at a point.
y = 1
slope = 0
derivative of 1 = 0

- 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

hmm derivatives are not always infinitesimal, but what they call dx is.

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- anonymous

Is it the slope of anything, or just curves?

- zzr0ck3r

in 2d it is a slope of the curve given its differentiable there.

- zzr0ck3r

at that point.

- 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

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

but this small change is not the derivative

- anonymous

can you tell me what must be learned before actually getting into the subject of derivatives?

- zzr0ck3r

nothing really, to understand it. But algebra before you can play with it

- anonymous

ok, thanks

- zzr0ck3r

how do we find slope?

- anonymous

of what?

- zzr0ck3r

rise/over run right?

- anonymous

of line is y1-y2/x1-x2

- zzr0ck3r

right

- zzr0ck3r

that is two points

- zzr0ck3r

now do the same thing with one point

- zzr0ck3r

x-x/y-y right?

- 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

with 1 point, wouldnt it be y1/x1?

- zzr0ck3r

actually gradient points in the "fastest" derivative, they are not the same.

- anonymous

The gradient is none existent because you are talking about 1 point. There is no change

- zzr0ck3r

1 point, wouldnt it be y1/x1?

- 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

calculus deals with that problem:)

- anonymous

As i have already mentioned above, the derivative is the rate of change. If you have 1 point there is no change.

- 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

you most certainly can have a derivative at one point

- anonymous

|dw:1370038095851:dw|

- zzr0ck3r

^^^^ that thing is dealing with the divide by 0 problem

- 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

Thank you zzr0ck3r, btw are you a teacher or student?

- zzr0ck3r

both

- zzr0ck3r

well I have to teach to graduate:)

- anonymous

lol, i am only in 9th grade :|

- zzr0ck3r

wow very cool.

- zzr0ck3r

I could not solve 3x = 6 in 9th grade:)

- anonymous

That is hard to believe >.>

- anonymous

You're in grad school?

- 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

Not because it's an easy equation, but because you seem very smart

- zzr0ck3r

I c what your saying sorry

- 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

Future, are you at harvard or MIT?

- zzr0ck3r

I was just trying to get her to think about the dividing by 0 thing

- zzr0ck3r

or him

- anonymous

im a guy

- anonymous

@FutureMathProfessor Ah the idiot who thinks that division by zero gives infinity strikes again. Everyone hide!

- zzr0ck3r

um im not graduate, but I am in a program where we follow a teacher, then teach.

- anonymous

future, are you in harvard or MIT?

- zzr0ck3r

I doubt anyone doing this in their free time are idiots

- anonymous

I was going to say. If you were at MIT I would come over and say hi, but I guess not

- zzr0ck3r

ha im old and didn't graduate high school MIT would not have taken me.

- 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

what is stackexchange?

- zzr0ck3r

find me a happy man and one that hangs out at the stock exchange and tell me who is smarter

- anonymous

o stock exchange ok

- zzr0ck3r

im giving you pearls here, listen up

- zzr0ck3r

lol

- anonymous

ok im listening, what were you going to say?

- zzr0ck3r

not u

- anonymous

well, i gtg thanks for the help everyone

- zzr0ck3r

np

- zzr0ck3r

p.s @yoanjm1 kahnacademy!

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