derivative f(x)=arccos(e^x)

解答

导数

f (x) = arccos (e^{x})

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

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

x \to 0 lim (\frac{6 x ^{2}}{x ^{2}})

\frac{\partial}{\partial x} (e^{- x^{5} - y^{3}})

y + 2 y^{^{'}} + 5 y = 4 \cdot e^{- t} \cdot cos (2 t)

d er i v a t i v e \frac{x - 2}{x - 2}