derivative (11)/(sqrt(x))

解答

导数

\frac{11}{x}

- \frac{11}{2 x ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{11}{x})

将常数提出:

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

= 11 \frac{d}{d x} (\frac{1}{x})

使用指数法则:

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

= 11 \frac{d}{d x} (x^{- \frac{1}{2}})

使用幂法则:

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

= 11 (- \frac{1}{2} x^{- \frac{1}{2} - 1})

化简

11 (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{11}{2 x ^{\frac{3}{2}}}

= - \frac{11}{2 x ^{\frac{3}{2}}}

\int \frac{1}{9 - 2 x} d x

\frac{d}{d x} (ln ∣ 4 x ∣)

\frac{\partial}{\partial y} (sin (x) + e^{x y})

49 y^{^{''}} + 112 y^{^{'}} + 64 y = 0

\int 25 + x d x