derivative of ln(arctan(7x^5))

解答

\frac{d}{d x} (ln (arctan (7 x^{5})))

\frac{35 x ^{4}}{arctan ( 7 x ^{5} ) ( 49 x ^{10} + 1 )}

求解步骤

\frac{d}{d x} (ln (arctan (7 x^{5})))

使用连锁律:

\frac{1}{arctan ( 7 x ^{5} )} \frac{d}{d x} (arctan (7 x^{5}))

= \frac{1}{arctan ( 7 x ^{5} )} \frac{d}{d x} (arctan (7 x^{5}))

\frac{d}{d x} (arctan (7 x^{5})) = \frac{35 x ^{4}}{49 x ^{10} + 1}

= \frac{1}{arctan ( 7 x ^{5} )} \cdot \frac{35 x ^{4}}{49 x ^{10} + 1}

化简

\frac{1}{arctan ( 7 x ^{5} )} \cdot \frac{35 x ^{4}}{49 x ^{10} + 1} : \frac{35 x ^{4}}{arctan ( 7 x ^{5} ) ( 49 x ^{10} + 1 )}

= \frac{35 x ^{4}}{arctan ( 7 x ^{5} ) ( 49 x ^{10} + 1 )}

\int_{- \infty}^{0} \frac{1}{6 - 7 x} d x

\frac{d}{d x} (x^{2} sin (x^{2}))

\int \frac{1}{x ^{2} + 6 x + 12} d x

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

d er i v a t i v e f (x) = \frac{5}{x ^{3}}