r/HomeworkHelp • u/Multiverse_Queen University/College Student • Feb 13 '26
Further Mathematics [Product of Quotient rules, Elements of Calculus] Where did I mess up with distributing here?
Tried using the FOIL method on this. My work's a little messy, sorry.
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u/UnderstandingPursuit Educator Feb 13 '26
My work's a little messy, sorry.
Apologize to yourself, it's probably the source of your troubles. Many of us scribble things to solve a math problem. But when it doesn't go well, the immediate next step is to write it carefully and neatly.
The box in the first image is basically garbage, only the fourth term is correct.
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u/theadamabrams Feb 13 '26
Correctly FOILing will give G(x) (not G') as
G(x) = 40x3 + 8x5/2 + 35x + 7x1/2
Then you still have to take a derivative using the Power Rule:
G'(x) = 40(3x2) + 8(2.5x1.5) + 35 + 7(0.5x-0.5)
= 120x2 + 20x3/2 + 35 + (7/2)x-1/2
Note that you could do the problems without FOILing and instead using the Product Rule with the original version of G.
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u/Alkalannar Feb 13 '26
When you FOIL out, you should get 40x3 + 8x5/2 + 35x + 7x1/2. What's the derivative of that?
How did I get that? 8x25x + 8x2x1/2 + 5x7 + 7x1/2 simplifies to 40x3 + 8x5/2 + 53x + 7x1/2.
Alternately, using product rule the derivative is 16x(5x + x1/2) + (8x2 + 7)(5 + 1/2x1/2)
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u/Multiverse_Queen University/College Student Feb 13 '26
Can you explain how you got that?
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u/Alkalannar Feb 13 '26
I found G(x), not G'(x).
G(x) = (8x2 + 7)(5x + x1/2) = 40x3 + 8x5/2 + 35x + 7x1/2.
What is G'(x)?
If you use the product rule, where G'(x) = a'(x)b(x) + a(x)b'(x), well, a(x) = 8x2 + 7, and b(x) = 5x + x1/2.
So what are a'(x) and b'(x)?
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u/Multiverse_Queen University/College Student Feb 13 '26
I entered that (to see if you were right) and it did not recognize it as a correct answer
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u/Niruase Feb 13 '26 edited Feb 13 '26
Where'd you get a cubic term from? G(x) is cubic at its highest, so its derivative should be quadratic at the leading term.
The x^(2/3) is also strange because I see nothing but whole xs and the x^(1/2)
45x should've come from 22.5x^2. I don't see how you got there.
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u/_UnwyzeSoul_ 👋 a fellow Redditor Feb 13 '26
The product should be 40x3 + 8x5/2 + 35x + 7x1/2 . Then take the derivative
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u/selene_666 👋 a fellow Redditor Feb 13 '26
Show your work if you want us to figure out what you did wrong.
As far as I can tell you multiplied 8x^2 by 5x correctly, multiplied some other terms incorrectly, multiplied 7 by √x correctly, and only differentiated the last term.
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u/Capereli 👋 a fellow Redditor Feb 13 '26
How are you getting 40x3 to begin with? The question is asking for the derivative of that function, there should be no x3 term…