derivative of (5sqrt(x)/x)

解答

\frac{d}{d x} (\frac{5 x}{x})

- \frac{5}{2 x ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{5 x}{x})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{x}{x})

使用微分除法定则:

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

= 5 \cdot \frac{\frac{d}{d x} ( x ) x - \frac{d x}{d x} x}{x ^{2}}

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

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

= 5 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}}

化简

5 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}} : - \frac{5}{2 x ^{\frac{3}{2}}}

= - \frac{5}{2 x ^{\frac{3}{2}}}