derivative of arctan(ln(x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\int \frac{8}{x + 1} d x

\frac{\partial}{\partial x} (\frac{5}{5 x + 3 y})

in v erse l a pl a ce \frac{10}{s ( s + 2 ) ( s + 3 ) ^{2}}

x \to 0 - lim (x sin (\frac{1}{x}))