derivative (sqrt(s)-3)/(sqrt(s)+7)

解答

导数

\frac{s - 3}{s + 7}

\frac{5}{s ( s + 7 ) ^{2}}

求解步骤

\frac{d}{d s} (\frac{s - 3}{s + 7})

使用微分除法定则:

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

= \frac{\frac{d}{d s} ( s - 3 ) ( s + 7 ) - \frac{d}{d s} ( s + 7 ) ( s - 3 )}{( s + 7 ) ^{2}}

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

\frac{d}{d s} (s + 7) = \frac{1}{2 s}

= \frac{\frac{1}{2 s} ( s + 7 ) - \frac{1}{2 s} ( s - 3 )}{( s + 7 ) ^{2}}

化简

\frac{\frac{1}{2 s} ( s + 7 ) - \frac{1}{2 s} ( s - 3 )}{( s + 7 ) ^{2}} : \frac{5}{s ( s + 7 ) ^{2}}

= \frac{5}{s ( s + 7 ) ^{2}}

x \to - 2 lim (\frac{- 1}{- x ^{2} + 4})

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