derivative of-2/(5sqrt(x))

解答

\frac{d}{d x} (- \frac{2}{5 x})

\frac{1}{5 x ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (- \frac{2}{5 x})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{2}{5} \frac{d}{d x} (\frac{1}{x})

使用指数法则:

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

= - \frac{2}{5} \frac{d}{d x} (x^{- \frac{1}{2}})

使用幂法则:

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

= - \frac{2}{5} (- \frac{1}{2} x^{- \frac{1}{2} - 1})

化简

- \frac{2}{5} (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : \frac{1}{5 x ^{\frac{3}{2}}}

= \frac{1}{5 x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{x + 2}{ln ( x )})

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

\int_{0}^{1} x 1 - x d x

so l v e f or x, \frac{d ^{2} x}{d t ^{2}} + x = (t^{2} + t) sin (t)

s l o p e (- 5, 11), (- 10, 6)