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Math Help - derivative of 2(2^x)

  1. #1
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    derivative of 2(2^x)

    Would it be 0(2^xln2) or 2(2^xln2)

    It is so confusing....
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by cammywhite View Post
    Would it be 0(2^xln2) or 2(2^xln2)

    It is so confusing....
    2(2^xln2)

    \frac{d(2^{x+1})}{dx} = \frac{d(2(2^x))}{dx}

    Using Chain Rule:

    = \frac{2^xd(2)}{~dx} + \frac{ 2d(2^x)}{~dx}

    = 0 +Ans
    Differntiation of constant is 0 and that of the second term is your answer
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    did you mean to type 2^{2^x \ln 2} ?? if so, you need the chain rule. if you actually meant 2(2^x \ln 2), then no chain rule necessary. just note that 2 \ln 2 is a constant, and so we just have to worry about the derivative of 2^x, hence

    \frac d{dx} 2(2^x \ln 2) = 2 (\ln 2^2) \cdot 2^x = 2^{x + 1} (\ln 2)^2
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