Formulas

The natural base

\(e \approx 2.718282\)

The Power Rule

${\displaystyle \frac{d}{dt}{t}^n=n{t}^{n-1}}$

The Constant Multiple Rule

${\displaystyle \frac{d}{dt}cf\left(t\right)=c\frac{df}{dt}}$

The Sum Rule

${\displaystyle \frac{d}{dt}\left[f\left(t\right)+g\left(t\right)\right]=\frac{df}{dt}+\frac{dg}{dt}}$

Derivatives of exponential functions

${\displaystyle \frac{d}{dt}{e}^t=e^t}$

${\displaystyle \frac{d}{dt}{e}^{kt}={ke}^{kt}}$

${\displaystyle \frac{d}{dt}{Ae}^{kt}={kAe}^{kt}}$

${\displaystyle \frac{d}{dt}{b}^t=(\ln b)b^t}$