Name: 05-1 權力規則（Power rule | Derivative rules | AP Calculus AB | Khan Academy）
Uploaded: 2022-07-12T12:22:54.000Z
Duration: 3 min 54 s
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In this video, we will cover the power rule,

動名詞

it comes to taking derivatives, especially

of x plus delta x minus f of x, all of that over delta x.

to find the slope of a tangent line at any given point.

But we're going to see what the power rule is.

We won't have to take these sometimes complicated limits.

And we're not going to prove it in this video,

but we'll hopefully get a sense of how to use it.

And in future videos, we'll get a sense of why it makes sense

So the power rule just tells us that if I have some function,

f of x, and it's equal to some power of x, so x

to the n power, where n does not equal 0.

It can be positive, a negative, it could be-- it

The power rule tells us that the derivative of this, f prime

so you're literally bringing this out front, n times x,

and then you just decrement the power, times x

to make sure that that actually makes sense.

So let's ask ourselves, well let's say that f of x

So that's going to be 2 times x to the first power, which

let's say we have g of x is equal to x to the third power.

What is g prime of x going to be in this scenario?

Well, n is 3, so we just literally pattern match here.

So this is going to be 3 times x to the 3 minus 1 power,

or this is going to be equal to 3x squared.

have h of x. h of x is equal to x to the negative 100 power.

The power rule tells us that h prime of x

Well n is negative 100, so it's negative 100x

is equal to negative 100x to the negative 101.

And we are concerned with what is z prime of x?

Well once again, power rule simplifies our life,

2.571 times x to the 2.571 minus 1 power.

me make sure I'm not falling off the bottom of the page--

And in the next few videos, we will not only

expose you to more properties of derivatives,

we'll get a sense for why the power rule at least makes

And then also prove the power rule for a few cases.

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05-1 權力規則（Power rule | Derivative rules | AP Calculus AB | Khan Academy）

literally

scenario

situation

pattern