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Math Help - Trigonometric Differentiation Problem.

  1. #1
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    Trigonometric Differentiation Problem.

    Hi, for the life of me I cannot figure this one out.

    Find the derivative of sin^4 \sqrt{u}.

    This is what I tried to do:
    sin^4 \sqrt{u} = (sin\sqrt{u})^4
    =4(sin\sqrt{u})^3 [cos\sqrt{u}(${\textstyle \frac{1}{2}}u^\frac{-1}{2})]

    The answer in the book is 2\sqrt{u}sin^3 \sqrt{u} cos\sqrt{u}.
    How the **** did they get that? Thanks.
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  2. #2
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    Re: Trigonometric Differentiation Problem.

    Quote Originally Posted by KhanDisciple View Post
    Hi, for the life of me I cannot figure this one out.

    Find the derivative of sin^4 \sqrt{u}.

    This is what I tried to do:
    sin^4 \sqrt{u} = (sin\sqrt{u})^4
    =4(sin\sqrt{u})^3 [cos\sqrt{u}({ \frac{1}{2}}u^\frac{-1}{2})]

    The answer in the book is 2\sqrt{u}sin^3 \sqrt{u} cos\sqrt{u}.
    How the **** did they get that? Thanks.

    Note that 4\sin^3 (\sqrt{u}) \left[cos(\sqrt{u})\left(\frac{1}{2\sqrt{u}}\right) \right] is the correct answer.

    Also, because \sin ~\&~\cos are functions please use function notation, like \sin(x) ~\&~\cos(x)
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  3. #3
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    Re: Trigonometric Differentiation Problem.

    Thank you Plato. The answers appeared completely different to me, and in the future I will try to use the correct notation.
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