Name: Product rule | Derivative rules | AP Calculus AB | Khan Academy
Uploaded: 2022-07-12T12:40:51.000Z
Duration: 2 min 40 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...

of the fundamental ways of evaluating derivatives.

And all it tells us is that if we have a function that

can be expressed as a product of two functions-- so let's

say it can be expressed as f of x times g of x-- and we

want to take the derivative of this function,

that it's going to be equal to the derivative of one

let's say the derivative of the first one times

the second function plus the first function,

not taking its derivative, times the derivative

In each term, we took the derivative of one

and we multiplied the derivative of the first function

Now let's see if we can actually apply this to actually find

So let's say we are dealing with-- I don't know--

let's say we're dealing with x squared times cosine of x.

And we are curious about taking the derivative of this.

We are curious about what its derivative is.

can be expressed as a product of two functions.

We could set f of x is equal to x squared,

And we could set g of x to be equal to sine of x.

And we could think about what these individual derivatives

The derivative of f of x is just going to be equal to 2x

by the power rule, and the derivative of g of x

And so now we're ready to apply the product rule.

This is going to be equal to f prime of x times g of x.

is 2x times g of x, which is sine of x plus just

times the derivative of g, times cosine of x.

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Product rule | Derivative rules | AP Calculus AB | Khan Academy

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