derivative of ln(arctan(2x^5))

Lösung

\frac{d}{d x} (ln (arctan (2 x^{5})))

\frac{10 x ^{4}}{arctan ( 2 x ^{5} ) ( 4 x ^{10} + 1 )}

Schritte zur Lösung

\frac{d}{d x} (ln (arctan (2 x^{5})))

Wende die Kettenregel an:

\frac{1}{arctan ( 2 x ^{5} )} \frac{d}{d x} (arctan (2 x^{5}))

= \frac{1}{arctan ( 2 x ^{5} )} \frac{d}{d x} (arctan (2 x^{5}))

\frac{d}{d x} (arctan (2 x^{5})) = \frac{10 x ^{4}}{4 x ^{10} + 1}

= \frac{1}{arctan ( 2 x ^{5} )} \cdot \frac{10 x ^{4}}{4 x ^{10} + 1}

Vereinfache

\frac{1}{arctan ( 2 x ^{5} )} \cdot \frac{10 x ^{4}}{4 x ^{10} + 1} : \frac{10 x ^{4}}{arctan ( 2 x ^{5} ) ( 4 x ^{10} + 1 )}

= \frac{10 x ^{4}}{arctan ( 2 x ^{5} ) ( 4 x ^{10} + 1 )}

\int \frac{1}{6 x ^{5}} d x

d er i v a t i v e 3 \cdot 2^{2 x + 1}

\int_{0}^{1} r 1 - r^{2} d r

\int (\frac{x ^{3}}{x - 1}) d x

\frac{d}{d x} ((1 - x)^{3} - 3 x (1 - x)^{2})