derivative of arcsec(x/a)

解答

\frac{d}{d x} (arcsec (\frac{x}{a}))

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

求解步骤

\frac{d}{d x} (arcsec (\frac{x}{a}))

使用连锁律:

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

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

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

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

化简

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

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

\int_{- \infty}^{0} \frac{1}{5 - 8 x} d x

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

\int \frac{x ^{3}}{x ^{8} + 5} d x

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

in v erse l a pl a ce \frac{s + 1}{( s + 6 ) ^{2} \cdot ( s + 2 )}