derivative arcsin((sqrt(x^2-1))/x)

解答

导数

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

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

x \to 3 lim (3 x + 9)

\frac{d}{d x} (2 x e^{y})

\int - 4 d x

\frac{\partial}{\partial y} (3 x - 4 y)

\int e^{x} cos (n x) d x