Question

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

Answer 1

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

Answer 2

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.

Answer 3

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

Answer 4

Is it the slope of anything, or just curves?

Answer 5

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

Answer 6

at that point.

Answer 7

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

Answer 8

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.

Answer 9

but this small change is not the derivative

Answer 10

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

Answer 11

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

Answer 12

ok, thanks

Answer 13

how do we find slope?

Answer 14

of what?

Answer 15

rise/over run right?

Answer 16

of line is y1-y2/x1-x2

Answer 17

right

Answer 18

that is two points

Answer 19

now do the same thing with one point

Answer 20

x-x/y-y right?

Answer 21

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.

Answer 22

with 1 point, wouldnt it be y1/x1?

Answer 23

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

Answer 24

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

Answer 25

1 point, wouldnt it be y1/x1?

Answer 26

with one point we are finding the change in that point
so we have y_1 - y_1/x_1 - x_1 = 0/0

Answer 27

calculus deals with that problem:)

Answer 28

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

Answer 29

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

Answer 30

you most certainly can have a derivative at one point