Formulas

Chapter 3
Initial Value Problems

Formulas

This summary repeats derivative formulas from Chapter 2, but with some reorganization and renaming.

The Constant Multiple Rule

\frac{d}{d t} A f (t) = A \frac{d f}{d t}

, for any constant A

The Sum Rule

\frac{d}{d t} ⌈ f (t) + g (t) ⌉ = \frac{d f}{d t} + \frac{d g}{d t}

The Difference Rule

\frac{d}{d t} ⌈ f (t) - g (t) ⌉ = \frac{d f}{d t} - \frac{d g}{d t}

Derivatives of exponential functions

\frac{d}{d t} e^{k t} = k e^{k t}

, for any constant k

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

, for any positive constant b

Derivatives of Power Functions (the Power Rule)

\frac{d}{d t} t^{n} = n t^{n - 1}

Derivatives of polynomial functions

Combine the Power Rule, the Constant Multiple Rule, and the Sum Rule.