derivative of arctan(1/2 x)

Lösung

\frac{d}{d x} (arctan (\frac{1}{2} x))

\frac{2}{x ^{2} + 4}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{1}{2} x))

Vereinfache

arctan (\frac{1}{2} x) : arctan (\frac{x}{2})

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Vereinfache

\frac{1}{( \frac{x}{2} ) ^{2} + 1} \cdot \frac{1}{2} : \frac{2}{x ^{2} + 4}

= \frac{2}{x ^{2} + 4}

\int \frac{x + 3}{x ^{2} + 1} d x

\frac{d y}{d x} - \frac{2}{x} y = x^{2} - 1

ma c l a u r in x^{2} cos (x^{5})

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\int \frac{sin ( x )}{cos ^{8} ( x )} d x