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Math Help - The Product Rule, am I on the right track?

  1. #1
    Junior Member
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    The Product Rule, am I on the right track?

    Hi all,

    I've been asked to use the product rule to show that the function

    g(x)=(1+2sinx)e^{\frac{1}{2}x+cosx}

    has derivative

    g'(x)=\frac{1}{2}(4cos^{2}x+4cosx-3)e^{\frac{1}{2}x+cosx}

    have I started right with

    g'(x)=(2cosx)(e^{\frac{1}{2}x+cosx})+(1+2sinx)[(e^{\frac{1}{2}x+cosx})(\frac{1}{2}-sinx)]

    Many thanks all.
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  2. #2
    MHF Contributor
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    Re: The Product Rule, am I on the right track?

    Looks okay to me. You have some algebra in your future.
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  3. #3
    Junior Member bondesan's Avatar
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    Re: The Product Rule, am I on the right track?

    It looks all right so far. Now you should distribute the product and use the trigonometrical identity to exchange sines for cosines.
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  4. #4
    Junior Member
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    Re: The Product Rule, am I on the right track?

    Thank you both, I very much appreciate it. I will continue with it this evening.
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