(\partial)/(\partial x)(v/x)

解答

\frac{\partial}{\partial x} (\frac{v}{x})

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

求解步骤

\frac{\partial}{\partial x} (\frac{v}{x})

将

v

视为常数

将常数提出:

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

= v \frac{\partial}{\partial x} (\frac{1}{x})

使用指数法则:

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

= v \frac{\partial}{\partial x} (x^{- 1})

使用幂法则:

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

= v (- 1 \cdot x^{- 1 - 1})

化简

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

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

\frac{d}{d x} (\frac{x - 2}{x ^{2} - 2 x + 4})

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

\int x 5^{x^{2}} d x

f (x) = 5 cos^{2} (x)

x \to 2 lim (2 - x)