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Beliebt Rechnen >

derivative arctan(sqrt(x))

Lösung

ableitung von

arctan (x)

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

limit as n approaches infinity of (3n)/n

n \to \infty lim (\frac{3 n}{n})

integral of (x-2)/(3x+6)

\int \frac{x - 2}{3 x + 6} d x

integral of (x^3)/(x^2-36)

\int \frac{x ^{3}}{x ^{2} - 36} d x

integral of sqrt(y/3)

\int \frac{y}{3} d y

integral from 0 to 1 of (10y)/(e^{2y)}

\int_{0}^{1} \frac{10 y}{e ^{2 y}} d y