derivative of-arctan(x+2arccot(x)-ln(x))

解答

\frac{d}{d x} (- arctan (x) + 2 arccot (x) - ln (x))

- \frac{3}{x ^{2} + 1} - \frac{1}{x}

求解步骤

\frac{d}{d x} (- arctan (x) + 2 arccot (x) - ln (x))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (arctan (x)) + \frac{d}{d x} (2 arccot (x)) - \frac{d}{d x} (ln (x))

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

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

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

= - \frac{1}{x ^{2} + 1} - \frac{2}{x ^{2} + 1} - \frac{1}{x}

合并分式

- \frac{1}{x ^{2} + 1} - \frac{2}{x ^{2} + 1} : - \frac{3}{x ^{2} + 1}

= - \frac{3}{x ^{2} + 1} - \frac{1}{x}

\int \frac{6}{x ln ( 2 x )} d x

\frac{\partial}{\partial x} (arcsin (\frac{y}{x}))

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

n = 1 \sum \infty \frac{5}{2 ^{n} + 1}

\frac{\partial}{\partial x} (\frac{( x y )}{x + y})