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 February 23rd, 2012, 04:17 AM #1 Newbie   Joined: Feb 2012 Posts: 1 Thanks: 0 Simple diff problem f(x)=10,000/(1+9e^-0.9x) find the first derivative of this function
February 23rd, 2012, 05:08 AM   #2
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Re: Simple diff problem

Quote:
 Originally Posted by zacmz f(x)=10,000/(1+9e^-0.9x) find the first derivative of this function
$f(x)=\frac{10.000}{1+9e^{-0.9x}}$
$\Rightarrow \frac{df(x)}{dx}=10.000 \frac{d}{dx}\left(\frac{1}{1+9e^{-0.9x}}\right)$
$=10.000 \frac{d}{dx}\left[(1+9e^{-0.9x})^{-1}\right]$
$=-10.000 \frac{1}{(1+9e^{-0.9x})^2} \frac{d}{dx}\left(1+9e^{-0.9x}\right)$
$=-10.000 \frac{-8.1e^{-0.9x}}{(1+9e^{-0.9x})}$
$=\frac{81000e^{-0.9x}}{(1+9e^{-0.9x})^2}$

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