derivative (3sqrt(x))/x

解答

导数

\frac{3 x}{x}

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

求解步骤

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

将常数提出:

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

= 3 \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}}

= 3 \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

= 3 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}}

化简

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

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

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