burhan101
Help me find the derivative of this function



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burhan101
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\[\huge A(t)= 20\sin^2(\frac{ t }{ 1000\pi })\]

bahrom7893
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Use power + chain rules

bahrom7893
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This is a very straightforward question.

burhan101
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dw:1371609626141:dw

burhan101
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like that?

bahrom7893
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you forgot the final chain rule

primeralph
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dw:1371609898205:dw

burhan101
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@bahrom7893 what do you mean?

bahrom7893
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dw:1371610057029:dw

primeralph
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dw:1371610058623:dw

burhan101
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@bahrom7893 wait i dont get it tho, why the extra fraction :S

bahrom7893
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derivative of dw:1371610223598:dw

bahrom7893
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dw:1371610328327:dw

burhan101
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dw:1371610801029:dw @bahrom7893

bahrom7893
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Noooo

Abhishek619
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dw:1371610749100:dw

bahrom7893
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Guys stop confusing him. Burhan, your first answer was right. You just forgot to add in that fraction.

burhan101
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How do i simplify further ?

bahrom7893
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just use algebra, cancel out some fractions.

burhan101
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howww im really confused !!

burhan101
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The answer key says it should be \[\huge A'(t) = \frac{ 1 }{ 50\pi }\sin (\frac{ t }{ 50\pi })\]

burhan101
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@bahrom7893

bahrom7893
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2Sin(x)Cos(x) = ? (double angle formula)

burhan101
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if i just simplify that fraction to 'x' then
=20((2sinx)(cosx)(x))
=20(xsinx)

primeralph
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.just use what I gave if you're still confused....

bahrom7893
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dw:1371612098284:dw

bahrom7893
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so according to our calculations, the answer should be:
dw:1371612290008:dw
which seemed right. the book might have a typo

primeralph
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........which is what I said 40 minutes ago........
dw:1371612421231:dw

bahrom7893
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lol

burhan101
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thanks both !@bahrom7893 @primeralph

primeralph
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You're very welcome.

bahrom7893
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np my friend :)

burhan101
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b) What is the first value of t greater than 0 for which the derivative is equal to 0?

burhan101
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@primeralph

bahrom7893
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set the derivative equal to 0, then check the signs nearby

burhan101
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@primeralph what does that mean ^ ?

primeralph
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for it to equal zero, you have to shift t by the period pi

primeralph
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dw:1371615489438:dw