(\partial)/(\partial x)(-y/x)

解答

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

\frac{y}{x ^{2}}

求解步骤

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

将

y

视为常数

将常数提出:

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

= - y \frac{\partial}{\partial x} (\frac{1}{x})

使用指数法则:

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

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

使用幂法则:

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

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

化简

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

= \frac{y}{x ^{2}}

t an g e n t f (x) = \frac{( x )}{x - 4}

\frac{\partial}{\partial x} (sin (x^{2} + 5))

(8 - r^{2}) d r = r^{3} sin (θ) d θ

\int_{0}^{1} \frac{x - 6}{x ^{2} - 6 x + 8} d x

3 x \frac{d y}{d x} = x^{2} - 4