derivative of (x+2/x)

解答

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

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

求解步骤

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

使用微分除法定则:

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

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

\frac{d}{d x} (x + 2) = 1

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

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

化简

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

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

x \to 4 lim (\frac{∣ x - 4 ∣}{4 - x})

\frac{\partial}{\partial x} (2 x + y - 2)

\frac{d}{d x} (a e^{x} + b)

\frac{\partial}{\partial y} (x y e^{- 2 y})

y^{^{'''}} - 2 y^{^{''}} - 48 y^{^{'}} = 0