derivative of ln(arctan(9x^4))

Lösung

\frac{d}{d x} (ln (arctan (9 x^{4})))

\frac{36 x ^{3}}{arctan ( 9 x ^{4} ) ( 81 x ^{8} + 1 )}

Schritte zur Lösung

\frac{d}{d x} (ln (arctan (9 x^{4})))

Wende die Kettenregel an:

\frac{1}{arctan ( 9 x ^{4} )} \frac{d}{d x} (arctan (9 x^{4}))

= \frac{1}{arctan ( 9 x ^{4} )} \frac{d}{d x} (arctan (9 x^{4}))

\frac{d}{d x} (arctan (9 x^{4})) = \frac{36 x ^{3}}{81 x ^{8} + 1}

= \frac{1}{arctan ( 9 x ^{4} )} \cdot \frac{36 x ^{3}}{81 x ^{8} + 1}

Vereinfache

\frac{1}{arctan ( 9 x ^{4} )} \cdot \frac{36 x ^{3}}{81 x ^{8} + 1} : \frac{36 x ^{3}}{arctan ( 9 x ^{4} ) ( 81 x ^{8} + 1 )}

= \frac{36 x ^{3}}{arctan ( 9 x ^{4} ) ( 81 x ^{8} + 1 )}

t a y l or f (x) = ln (x)

x \to 0 lim (x ln (3 x))

k \to 0 lim (\frac{( 2 z + 3 k ) ^{3} - 4 k ^{2} z}{2 z ( 2 z - k ) ^{2}})

\int_{2}^{\infty} \frac{2}{x ^{2} - x} d x

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