derivative of ln(arctan(8x^5))

Lösung

\frac{d}{d x} (ln (arctan (8 x^{5})))

\frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}

Schritte zur Lösung

\frac{d}{d x} (ln (arctan (8 x^{5})))

Wende die Kettenregel an:

\frac{1}{arctan ( 8 x ^{5} )} \frac{d}{d x} (arctan (8 x^{5}))

= \frac{1}{arctan ( 8 x ^{5} )} \frac{d}{d x} (arctan (8 x^{5}))

\frac{d}{d x} (arctan (8 x^{5})) = \frac{40 x ^{4}}{64 x ^{10} + 1}

= \frac{1}{arctan ( 8 x ^{5} )} \cdot \frac{40 x ^{4}}{64 x ^{10} + 1}

Vereinfache

\frac{1}{arctan ( 8 x ^{5} )} \cdot \frac{40 x ^{4}}{64 x ^{10} + 1} : \frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}

= \frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}

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

\int 3 x \cdot (x + 1)^{2} d x

(1 + y^{2} + x y^{2}) d x + (x^{2} y + y + 2 x y) d y = 0

\frac{d}{d x} (x^{0.6})

a re a y = x, y = 12 x, x = 9