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Math Help - Derivative problem

  1. #1
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    Derivative problem

    Hello, I have the following expression I'd like to derive in terms of 'x'. 'k' is just a constant.

    <br />
f(x) =  2(\frac{\sin{x}+1}{2})^k<br />

    I haven't done this sort of maths for a while, any pointers?
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  2. #2
    Moo
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    Hello,

    f(x)=2(u(x))^k

    The derivative of such a function is :

    f'(x)=2ku'(x)(u(x))^{k-1}

    u(x)=\frac{\sin(x)+1}{2}=\frac{\sin(x)}{2}+\frac{1  }{2}

    So u'(x)=\frac{\cos(x)}{2}

    And then substitute it in f'(x)
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  3. #3
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    Ah, great! Thanks.

    This is what I got:

    <br />
f'(x) = k\cos{x}\Bigl(\frac{\sin{x}+1}{2}\Bigr)^{k-1}<br />

    Is it correct?
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  4. #4
    Moo
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    Yes it is ^^

    (hoping that k is different from 0)
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