derivative of sqrt(arctan(x/2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (arctan (\frac{x}{2})) = \frac{2}{x ^{2} + 4}

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

Vereinfache

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

= \frac{1}{arctan ( \frac{x}{2} ) ( x ^{2} + 4 )}

\frac{\partial}{\partial y} (\frac{2 x}{y ^{2}})

y^{^{'}} = 8 (y^{2} + 1)

f (x) = 6 x^{\frac{1}{2}}

\int cos (5 x - 1) d x

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