Name: Worked example: Product rule with table | Derivative rules | AP Calculus AB | Khan Academy
Uploaded: 2022-07-12T12:40:54.000Z
Duration: 3 min 8 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] The following tables lists the values

of functions f and h, and of their derivatives,

f prime and h prime for x is equal to three.

the value of the function is six, f of three is six,

h of three is zero, f prime of three is six,

And now they want us to evaluate the derivative

with respect to x of the product of f of x and h of x

g of x as being equal to the product of f of x

this expression is the derivative of g of x.

So we could write g prime of x is equal to the derivative

and which is what we want to evaluate at x equals three.

Well, to do that, let's go first up here.

Let's just think about what this is doing.

with respect to x of the product of two functions

Well, if we're taking the derivative of the product

of two functions, you could imagine that the

So I'm just gonna restate the product rule.

This is going to be equal to the derivative

times the second function, not taking its derivative.

Plus the first function, not taking its derivative,

f of x, times the derivative of the second function,

So if you're trying to find g prime of three,

And lucky for us, they give us what all these things

f prime of three, right over here, they tell us.

f prime when x is equal to three is equal to six.

h of three, when x is three, the value of our

So this first term is you just get six times zero,

which is gonna be zero, but we'll get to that.

Well, the function when x is equal to three,

Or you could say this is h prime of three.

This is going to evaluate to six times zero,

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Worked example: Product rule with table | Derivative rules | AP Calculus AB | Khan Academy

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