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Math Help - Trig Differentiation with Chain Rule

  1. #1
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    Trig Differentiation with Chain Rule

    Hi,

    I'm having trouble finding the derivative for:

    g(x) = [sec(.5x)tan(.5x)]

    It's a lot of steps, but my answer is: .5(sec(.5x)+tan(.5x))[.5sec(.5x)]

    I'm very sure that it is incorrect. since I just basically used the chain rule for the first function, then multiplying it with the chain rule derivative of the second function.

    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by Enderless View Post
    Hi,

    I'm having trouble finding the derivative for:

    g(x) = [sec(.5x)tan(.5x)]

    It's a lot of steps, but my answer is: .5(sec(.5x)+tan(.5x))[.5sec(.5x)]

    I'm very sure that it is incorrect. since I just basically used the chain rule for the first function, then multiplying it with the chain rule derivative of the second function.

    Any help would be appreciated.
    Use the product rule first:
    g^{\prime}(x) = [sec(0.5x)]^{\prime} \cdot tan(0.5x) + sec(0.5x) \cdot [tan(0.5x)]^{\prime}

    = [sec(0.5x)tan(0.5x) \cdot 0.5] \cdot tan(0.5x) + sec(0.5x) \cdot [sec^2(0.5x) \cdot 0.5]

    = 0.5sec(0.5x)tan^2(0.5x) + 0.5sec^3(0.5x)

    -Dan
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