derivative y= 1/(arctan(x))

解答

导数

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

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

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

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

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

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

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

化简

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

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

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

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

\int_{- 2}^{2} 4 d x

\frac{\partial}{\partial y} (- x^{4} + 4 x y - y^{4} + 1)

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