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En
 one year ago
PLEASE HELP!
find the derivative of w=sin^4ycos^4y.
my final answer is 4sin^3cos^3y * cos2y.
but the answer written in my book is 1/2sin^3
(2y)cos(2y)
En
 one year ago
PLEASE HELP! find the derivative of w=sin^4ycos^4y. my final answer is 4sin^3cos^3y * cos2y. but the answer written in my book is 1/2sin^3 (2y)cos(2y)

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1I recommend using the double angle identity first to rewrite w then differentiate

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\sin(2y)=2 \sin(y) \cos(y) \\ \frac{1}{2} \sin(2y)=\sin(y) \cos(y) \\ w=( \frac{1}{2} \sin(2y))^4 \]

En
 one year ago
Best ResponseYou've already chosen the best response.0w = sin^4y cos^4y dw/dy = 4 sin^3y* cos^5y  4 cos^3y* sin^5y = 4 sin^3y cos^3y[ cos^2y  sin^2y] = 4 sin^3y cos^3y * cos2y = 1/2*(2siny cosy)^3 * cos2y = 1/2 sin^3(2y) cos2y someone answere it this way... i just dont get where the 1/2 came from.. please explain

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[2\sin(y)\cos(y)=\sin(2y)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@En dont copy and past from yahoo answers.. its best to solve them yourself for you can learn more.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=derivative+of+sin^4y+cos^4y

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[4=\frac{1}{2}(2)^3 \text{ they just rewrote 4 }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1np i was kind of confused at first i thought it was your solution

freckles
 one year ago
Best ResponseYou've already chosen the best response.1@En I feel like that first way I suggested might be a little easier

En
 one year ago
Best ResponseYou've already chosen the best response.0i solved the 4sin^3cos^3y * cos2y i just got confused in the simplifying process :)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[w=(\frac{1}{2} \sin(2y))^4 \\ w'=4(\frac{1}{2}\sin(2y))^{3}(\frac{1}{2} \sin(2y))' \\ w'=4(\frac{1}{2}\sin(2y))^3 \frac{1}{2} \cdot 2 \cos(2y) \\ w'=4 (\frac{1}{2})^3 \sin^3(2y) \cos(2y) \\ w'=\frac{4}{8} \sin^3(2y) \cos(2y) \\ w'=\frac{1}{2} \sin^3(2y) \cos(2y)\] just a whole bunch of chain rule

En
 one year ago
Best ResponseYou've already chosen the best response.0Where did you get the w=1/2sin(2y))^4? @freckles

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the double angle identity 2sin(y)cos(y)=sin(2y) so sin(y)cos(y)=1/2*sin(2y)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so (sin(y) cos(y))^4=(1/2*sin(2y))^4

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and (sin(y) cos(y))^4=sin^4(y)*cos^4(y)

En
 one year ago
Best ResponseYou've already chosen the best response.0where did the "1/2" came from?

freckles
 one year ago
Best ResponseYou've already chosen the best response.12sin(y)cos(y) is equal to sin(2y) do you understand this part?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1divide both sides by 2 sin(y)cos(y) is equal to 1/2*sin(2y)
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