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Math Help - differentiate y=a*exp^(-x/b)+c

  1. #1
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    differentiate y=a*exp^(-x/b)+c

    I need to find the derivative of the following function......

    y=a*(exp^(-x/b))+c


    can anyone please help me!

    Many thanks
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  2. #2
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    Quote Originally Posted by Confused169 View Post
    I need to find the derivative of the following function......

    y=a*(exp^(-x/b))+c


    can anyone please help me!

    Many thanks
    The derivative of a e^{kx} is k a e^{kx}. In your problem k = -1/b ......
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Confused169 View Post
    I need to find the derivative of the following function......

    y=a*(exp^(-x/b))+c


    can anyone please help me!

    Many thanks
    Alternatively you could go this route

    y=ae^{\frac{-x}{b}}+C

    Disregarding the C as 0 when differentiated we just need to tackle

    y=ae^{\frac{-x}{b}}\Rightarrow\ln(y)=\ln\bigg(ae^{\frac{-x}{b}}\bigg)=\ln(a)-\frac{x}{b}

    so differentinag the left side implicitly and the right side regularly we get

    \frac{y'}{y}=\frac{-1}{b}

    so seeing that y is the original equation we get

    y'=\frac{-a}{b}e^{\frac{-x}{b}}
    Last edited by Mathstud28; June 4th 2008 at 10:29 AM.
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  4. #4
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    Cheers guys.... thanks for the speedy reply.
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