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Math Help - chain rule problem

  1. #1
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    chain rule problem

    Find the derivative of the function. y = 2^3 - x^2


    cant get the right answer, i think its partly due to me not knowing the derivative of 2^x.

    I did:

    outside function = 2^x
    outside deriv.= 2^xlog(2) <----this is what i got from an online deriv. calc

    inside = 3-x^2
    inside deriv = -2x
    ------------------
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  2. #2
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    Please post the original function in a clear manner.
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  4. #4
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    I dont undersand the whole inside and outside thing you got going on, but i know that since it is an additive functionjust take the derivative of each term. Like you did in the inside part and put them together.
    The answer would be:

    y'= 3x^2-2x

    which folows f(x)= x^(n)

    nx^(n-1)
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  5. #5
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    Quote Originally Posted by Evan.Kimia View Post
    oh sorry i get your question now
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  6. #6
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    Quote Originally Posted by Evan.Kimia View Post
    Take y=2^(3-x^2)

    youre probably making a simple mistake

    -16*log(2)*x/2^x^2
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  7. #7
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    y= 2^{3-x^2}

    make  u = 3-x^2 \Rightarrow \frac{du}{dx} = -2x

    and y= 2^u \Rightarrow \frac{dy}{du} = \ln(2)2^u

     \frac{dy}{dx} = \frac{dy}{du}\times \frac{du}{dx}

     \frac{dy}{dx} = \ln(2)2^u\times -2x

     \frac{dy}{dx} = \ln(2)2^{3-x^2}\times -2x

     \frac{dy}{dx} = -2\ln(2)x2^{3-x^2}
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