derivative of arctan(ln(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (x^{4} y^{8} + 4 x^{5} y)

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

\frac{d}{d x} (5 lo g_{2} (x))

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

in v erse l a pl a ce \frac{8}{( s - 1 ) ^{3}}