derivative of (-y/x)

解答

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

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

求解步骤

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

化简

\frac{- y}{x} : - \frac{y}{x}

= \frac{d}{d x} (- \frac{y}{x})

将常数提出:

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

= - \frac{d}{d x} (\frac{y}{x})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

= - \frac{\frac{d y}{d x} x - 1 \cdot y}{x ^{2}}

化简

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

s l o p e (- 3, 7), (2, - 5)

d er i v a t i v e f (x) = 1 - 3 x^{2}

\frac{d}{d x} (\frac{2 x + 3}{3 x + 2})

cos^{2} (x) sin (x) \frac{d y}{d x} + cos^{3} (x) y = 1

t an g e n t x^{3} - 2 x^{2} - 3 x