derivative of (3-2x/(3+2x))

解答

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

- \frac{12}{( 3 + 2 x ) ^{2}}

求解步骤

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

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

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

\frac{d}{d x} (3 + 2 x) = 2

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

化简

\frac{( - 2 ) ( 3 + 2 x ) - 2 ( 3 - 2 x )}{( 3 + 2 x ) ^{2}} : - \frac{12}{( 3 + 2 x ) ^{2}}

= - \frac{12}{( 3 + 2 x ) ^{2}}

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