derivative f(x)=(2x+5)/(x+2)*2x-5

解答

导数

f (x) = \frac{2 x + 5}{x + 2} \cdot 2 x - 5

\frac{2 ( 2 x ^{2} + 8 x + 10 )}{( x + 2 ) ^{2}}

求解步骤

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

化简

\frac{2 x + 5}{x + 2} \cdot 2 x - 5 : \frac{2 x ( 2 x + 5 )}{x + 2} - 5

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (\frac{2 x ( 2 x + 5 )}{x + 2}) = \frac{2 ( 2 x ^{2} + 8 x + 10 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (5) = 0

= \frac{2 ( 2 x ^{2} + 8 x + 10 )}{( x + 2 ) ^{2}} - 0

化简

= \frac{2 ( 2 x ^{2} + 8 x + 10 )}{( x + 2 ) ^{2}}

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