derivative (x-3)/(sqrt(x)-\sqrt{3)}

解答

导数

\frac{x - 3}{x - 3}

\frac{x - 2 3 x + 3}{2 x ( x - 3 ) ^{2}}

求解步骤

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

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 - 3 ) ( x - 3 ) - \frac{d}{d x} ( x - 3 ) ( x - 3 )}{( x - 3 ) ^{2}}

\frac{d}{d x} (x - 3) = 1

\frac{d}{d x} (x - 3) = \frac{1}{2 x}

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

化简

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

= \frac{x - 2 3 x + 3}{2 x ( x - 3 ) ^{2}}

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