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Math Help - An otherwise simple derivative problem...

  1. #1
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    An otherwise simple derivative problem...

    Calculate:
    d/dx[(e^x + xsin(x))/(tan(x))]

    I got this far:
    [tan(x) * e^x + 1cos(x)]-[e^x + xsin(x) * sex^2(x)]/[tan(x)]

    But my book says it's supposed to be;
    [tan(x) * e^x + sin(x) + xcos(x)]-[e^x + xsin(x) * sex^2(x)]/[tan(x)]

    How come those things...?
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  2. #2
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    Re: An otherwise simple derivative problem...

    Quote Originally Posted by Nervous View Post
    Calculate:
    d/dx[(e^x + xsin(x))/(tan(x))]
    this is the correct derivative ,,,

    \frac{\tan{x}\left(e^x + x\cos{x} + \sin{x}) - \sec^2{x}(e^x + x\sin{x})}{\tan^2{x}}

    note that the derivative of the numerator, (e^x + x\sin{x}), is (e^x + x\cos{x} + \sin{x}) ... you must use the product rule with x\sin{x}
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