Multiplying functions - How to find the product of functions

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In this video we're talking about how to find the product of two functions. In other words, if we want to multiply two functions together, how do we do it and what will we get when we do?
Skip to section:
0:12 // What is the "product of functions"?
0:23 // How to do you write the product of two functions?
1:01 // Multiplying functions that are numbers (constants)
1:31 // Multiplying functions that have variables
2:35 // Finding fg(2): the value of the product function at x=2
When you have multiple functions, you can use some simple rules to find their sum, difference, product, or quotient. In this video we're going to focus on how to find the product of two functions.
As you might guess, finding the product of functions is as simple multiplying the functions together. When you multiply two functions together, you'll get a third function as the result, and that third function will be the product of the two original functions.
For example, if you multiply f(x) and g(x), their product will be h(x)=fg(x), or h(x)=f(x)g(x). You can also evaluate the product at a particular point. So if you want to know the value of the product at x=2, you can plug x=2 into the product function h(x) to find h(2)=fg(2)=f(2)g(2).
Alternately, instead of first finding the product function, and then evaluating at x=2, you could first evaluate both f(x) and g(x) at x=2, and then multiply those results together to get the product h(2).
Music by Joakim Karud: / joakimkarud
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[@kristakingmath]

How to multiply functions together to find their product! :)

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[@kristakingmath]

Thanks George! I plan to continue. :)

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[@kristakingmath]

I'm so glad you're liking the videos, Lee! I've already got some videos on Laplace, but I need to make some for Fourier, too. :)

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[@AlexBerg1]

Looks exactly like function composition, common in functional programming. Also related to category theory, composing arrows. I wonder if there are other ways to combine two functions, other than multiplication...

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Hello, what does differentiating a product of function mean?

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*Hello Krista, you're a math icon.Just a quick question though : Is the product of two functions the same as a composite function? Thank you.*

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ivor worrell No

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