Simple derivation: F(t)=1-e^(-1/t), E(t)=dF/dt=e^(-1/t)(....

[f0rked]

Could anyone tell me if this is correct? Thanks! It's been a while since I've done any differentiation and I'm a bit rusty.

 

[soroban]

Re: Simple derivation.

Hello, f0rked!

Not quite . . .

$\displaystyle F(t) \:=\:1-e^{-\frac{1}{t}}$

$\displaystyle \text{Then: }\;\frac{dF}{dt} \;=\;-e^{-\frac{1}{t}}\cdot\frac{d}{dt}\left(-\frac{1}{t}\right)$

. . $\displaystyle \frac{d}{dt}\left(-\frac{1}{t}\right) \;=\;\frac{d}{dt}\left(-t^{-1}\right) \;=\;t^{-2} \;=\;\frac{1}{t^2}$


$\displaystyle \text{Therefore: }\;\frac{dF}{dt} \;=\;-e^{-\frac{1}{t}}\cdot\frac{1}{t^2} \;=\;-\frac{e^{-\frac{1}{t}}}{t^2}$

 

[f0rked]

Re: Simple derivation.

Thanks a lot, that was really helpful!