(\partial)/(\partial x)(2arctan(x))

Lösung

\frac{\partial}{\partial x} (2 arctan (x))

\frac{2}{x ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (2 arctan (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (arctan (x))

Wende die allgemeine Ableitungsregel an:

\frac{\partial}{\partial x} (arctan (x)) = \frac{1}{x ^{2} + 1}

= 2 \cdot \frac{1}{x ^{2} + 1}

Vereinfache

2 \cdot \frac{1}{x ^{2} + 1} : \frac{2}{x ^{2} + 1}

= \frac{2}{x ^{2} + 1}

\int \frac{x ^{2} + 8 x - 3}{x ^{3} + 3 x ^{2}} d x

\int \frac{1}{100 - t} d t

\int \frac{1}{x ^{2} - 8 x + 16} d x

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\frac{d}{d x} (\frac{( x + 1 ) ^{2}}{x})