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Math Help - differentiation

  1. #1
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    differentiation

    hey

    i got a problem with differentiation, and im not having much luck

    the question is if i have a exponential function

    y=12*0.5^x

    how would find y'
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  2. #2
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    Hello,

    Transform it with logarithms. You can't derivate correctly when there is x in the power.

    ln(ab)=ln(a)+ln(b)

    ln(a^b)=b ln(a)

    ;-)
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  3. #3
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    okay thanks

    so its = ln(12) +ln(0.5^x)
    = ln(12) + xln(0.5)
    =x ln(0.5) + ln(12)
    =x ln(0.5 * 12)
    =x ln(6)
    = 1.79x
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  4. #4
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    Quote Originally Posted by Quill View Post
    okay thanks

    so its = ln(12) +ln(0.5^x)
    = ln(12) + xln(0.5)
    =x ln(0.5) + ln(12)
    =x ln(0.5 * 12)
    =x ln(6)
    = 1.79x
    No.

    y = k \, (a^x) = k\, e^{\ln a^x} = k \, e^{x \ln a} which just has the form y = k \, e^{bx}. And you know how to differentiate that form, right?

    So you end up with \frac{dy}{dx} = k \, (\ln a) \, a^x. Capisce?

    A formula worth remembering.
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  5. #5
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    um i think i got it

    y=12*0.5^x
    =12(0.5^x)
    =12(e^ln0.5^x)
    =12(e^xln0.5)
    =12(ln0.5)0.5^x

    thanks again
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Quill View Post
    um i think i got it

    y=12*0.5^x
    =12(0.5^x)
    =12(e^ln0.5^x)
    =12(e^xln0.5)
    =12(ln0.5)0.5^x

    thanks again
    indeed. now that you know two ways to find the derivative of functions like this, it's time for the general rule.

    \frac d{dx}(a^x) = a^x \ln a where a > 0 is a constant
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  7. #7
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    thanks

    one last thing, when i graph it, i get an almost straight line, is that normal
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  8. #8
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    Quote Originally Posted by Quill View Post
    thanks

    one last thing, when i graph it, i get an almost straight line, is that normal
    It might look that way, depending on the scale you've used. But it most certainly is not a straight line.
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  9. #9
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    are yer that made it work

    thanks
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