Name: Worked example: Derivative of cos_(x) using the chain rule | AP Calculus AB | Khan Academy
Uploaded: 2022-09-09T14:51:50.000Z
Duration: 9 min 17 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

- [Voiceover] Let's say we have the function f of x

which is equal to cosine of x to the third power

Modal verbs - A2

what f prime of x is going to be equal to.

So we want to figure out f prime of x and as we will see,

the chain rule is going to be very useful here

I'm going to first just apply the chain rule

between what we're doing here and then what you might see

that is defined as essentially a composite function,

we are taking something to the third power.

It isn't just an x that we're taking to the third power.

We are taking a cosine of x to the third power.

So we're taking a function, you could view it this way,

and then we're inputting it in to another function

and so that's going to produce cosine of x,

and then we're going to input it into a function

that just takes things to the third power.

So it just takes things to the third power.

And so what are you going to end up with?

and then if we're taking u of x into the input

That's the same thing as v of cosine of x.

or the chain rule is what our brain should say.

if we're going to take the derivative of a function

that can be expressed as a composite function like this.

So just to be clear, we can write f of x.

I know I'm essentially saying the same thing

but I'm saying it in slightly different ways

so I'm going to try to write it in different ways.

and this is something that you will see in your textbooks.

so we could write that as v prime of u of x.

times the derivative of u with respect to x.

and so how do we evaluate it in this case?

Well, let me color code it in a similar way.

this outer thing that just takes things to the third power,

and I'll use it with more of the differential notation,

you could view this as the derivative of,

well, I'll write it a couple of different ways.

Subtitles ListPlay Video

Worked example: Derivative of cos_(x) using the chain rule | AP Calculus AB | Khan Academy

essentially

figure

multiple

situation