derivative of x/((1-2x^2))

解答

\frac{d}{d x} (\frac{x}{( 1 - 2 x ) ^{2}})

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

求解步骤

\frac{d}{d x} (\frac{x}{( 1 - 2 x ) ^{2}})

使用微分除法定则:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((1 - 2 x)^{2}) = - 4 (1 - 2 x)

= \frac{1 \cdot ( 1 - 2 x ) ^{2} - ( - 4 ( 1 - 2 x ) ) x}{( ( 1 - 2 x ) ^{2} ) ^{2}}

化简

\frac{1 \cdot ( 1 - 2 x ) ^{2} - ( - 4 ( 1 - 2 x ) ) x}{( ( 1 - 2 x ) ^{2} ) ^{2}} : \frac{1 + 2 x}{( 1 - 2 x ) ^{3}}

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

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