derivative of 19arctan(sqrt(x))

Lösung

\frac{d}{d x} (19 arctan (x))

\frac{19}{2 x ( x + 1 )}

Schritte zur Lösung

\frac{d}{d x} (19 arctan (x))

Entferne die Konstante:

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

= 19 \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}

= 19 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x}

Vereinfache

19 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x} : \frac{19}{2 x ( x + 1 )}

= \frac{19}{2 x ( x + 1 )}

d er i v a t i v e ln (\frac{6 x ^{2} + 5}{x ^{\frac{4}{5}}})

in v erse l a pl a ce \frac{s + 4}{s ^{2} + 2 s - 3}

d er i v a t i v e 5 x^{2} + 2 x + 6

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

y^{^{''}} - \frac{2}{x} y^{^{'}} - \frac{10}{x ^{2}} y = 0