derivative of (3x+1/(x-1))

解答

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

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

求解步骤

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

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

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

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

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

化简

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

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

\frac{\partial}{\partial x} (e^{x} sin (x))

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