Simple derivation: F(t)=1-e^(-1/t), E(t)=dF/dt=e^(-1/t)(....
- Thread starter f0rked
- Start date
Re: Simple derivation.
Hello, f0rked!
Not quite . . .
\(\displaystyle \text{Then: }\;\frac{dF}{dt} \;=\;-e^{-\frac{1}{t}}\cdot\frac{d}{dt}\left(-\frac{1}{t}\right)\)
. . \(\displaystyle \frac{d}{dt}\left(-\frac{1}{t}\right) \;=\;\frac{d}{dt}\left(-t^{-1}\right) \;=\;t^{-2} \;=\;\frac{1}{t^2}\)
\(\displaystyle \text{Therefore: }\;\frac{dF}{dt} \;=\;-e^{-\frac{1}{t}}\cdot\frac{1}{t^2} \;=\;-\frac{e^{-\frac{1}{t}}}{t^2}\)
Hello, f0rked!
Not quite . . .
\(\displaystyle \text{Then: }\;\frac{dF}{dt} \;=\;-e^{-\frac{1}{t}}\cdot\frac{d}{dt}\left(-\frac{1}{t}\right)\)
. . \(\displaystyle \frac{d}{dt}\left(-\frac{1}{t}\right) \;=\;\frac{d}{dt}\left(-t^{-1}\right) \;=\;t^{-2} \;=\;\frac{1}{t^2}\)
\(\displaystyle \text{Therefore: }\;\frac{dF}{dt} \;=\;-e^{-\frac{1}{t}}\cdot\frac{1}{t^2} \;=\;-\frac{e^{-\frac{1}{t}}}{t^2}\)
