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Math Help - Derivative help.

  1. #1
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    Derivative help.

    Find Dx^5y if y=cos(2x)-sin(2x). Thanks in advance.
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  2. #2
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    Quote Originally Posted by Ethereal Overlord View Post
    Find Dx^5y if y=cos(2x)-sin(2x). Thanks in advance.
    \frac{dy}{dx} = -sin(2x) \cdot 2 - cos(2x) \cdot 2 = -2(sin(2x) + cos(2x))

    And
    \frac{d}{dx}(x^5y) = 5x^4y + x^5 \frac{dy}{dx}

    So
    \frac{d}{dx}(x^5y) = 5x^4(cos(2x)-sin(2x)) + x^5(-2(sin(2x) + cos(2x))) = (-5x^4 - 2x^5)sin(2x) + (5x^4 - 2x^5)cos(2x) = x^4[ -(5 + x)sin(2x) + (5 - x)cos(2x)]

    -Dan

    PS I like the username!
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  3. #3
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    Awesome, thanks a bunch.
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