2.2 Elementare Ableitungsregeln

Potenzregel: $f (x) = x^{r} f^{'} (x) = r \cdot x^{r - 1}$

r \in R ∖ {0}

Faktorregel: $f (x) = C u (x) f^{'} (x) = C u^{'} (x)$
Konstantenregel: $f (x) = c f^{'} (x) = 0$
Summenregel: $f (x) = v (x) + v (x) f (x) = u^{'} (x) + v^{'} (x)$

Notizen:

\begin{array}{ll} \frac{1}{x^{3}} = x^{- 3} & \sqrt{x} = x^{\frac{1}{2}} \\ \frac{2}{x^{5}} = 2 \cdot x^{- 5} & \sqrt[3]{x} = x^{\frac{1}{3}} \\ \frac{1}{4 x^{2}} = \frac{1}{4} x^{- 2} & \sqrt[5]{x^{2}} = x^{\frac{2}{5}} \\ \sqrt[(2 x)^{2}]{} = (2 x)^{\frac{2}{5}} \end{array}

Allgemein: $\frac{1}{x^{n}} = x^{- n} \sqrt[n]{x} = x^{\frac{1}{n}}$