derivative of arccsc(e^x)

解答

\frac{d}{d x} (arccsc (e^{x}))

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

求解步骤

\frac{d}{d x} (arccsc (e^{x}))

使用连锁律:

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

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

\frac{d}{d x} (e^{x}) = e^{x}

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

化简

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

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

a re a 7 cos (8 x), 7 - 7 cos (8 x), [0, \frac{π}{8}]

t a y l or φ^{5} cos (φ^{2})

\frac{d}{d x} (\frac{2 ( x + 8 ) ( x - 6 )}{x ^{2} - 7 ^{2}})

\int \frac{5 sin ( x )}{x} d x

y^{^{'}} - \frac{2}{t} y = t^{3}