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Math Help - derivitive

  1. #1
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    Unhappy derivitive

    r(t) = cos^3 t + sin^3 t

    How do you find r'(t)? Would it be -3sin^2 t + 3 cos^2 t or something else?
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  2. #2
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    Quote Originally Posted by tdat1979 View Post
    r(t) = cos^3 t + sin^3 t

    How do you find r'(t)? Would it be -3sin^2 t + 3 cos^2 t or something else?
    You need to use the chain rule.

    \frac{d}{dt}(\cos^3{t}) = -3\sin{t}\cos^2{t}

    \frac{d}{dt}(\sin^3{t}) = 3\cos{t}\sin^2{t}.


    Therefore

    r'(t) = 3\cos{t}\sin^2{t} - 3\sin{t}\cos^2{t}

     = 3\cos{t}\sin{t}(\sin{t} - \cos{t}).
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