derivative of ln(arctan(x))

解答

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

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

求解步骤

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

使用连锁律:

\frac{1}{arctan ( x )} \frac{d}{d x} (arctan (x))

= \frac{1}{arctan ( x )} \frac{d}{d x} (arctan (x))

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

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

化简

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

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

\frac{d y}{d x} - 3 y = 0

n = 1 \sum \infty (- 0.7)^{n - 1}

\frac{\partial}{\partial t} (\frac{x}{t})

\int_{0}^{3} π (9 x^{2} - x^{4}) d x

x \to 1 lim (e^{6 x^{5} - 6 x})