derivative sqrt(arctan(x))

Lösung

ableitung von

arctan (x)

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{2}{3} x (a^{2} + x^{2})^{\frac{3}{2}} d x

d er i v a t i v e \frac{s - 1}{s + 7}

\int ln (1 + t) d t

\int 15 x^{2} e^{5 x^{3} - 6} d x

s \to 0 lim (\frac{- \frac{1}{s}}{1 + ( 3 + \frac{13}{s} ) ( \frac{7}{x s + 1} )})