derivative of x/((x-6^2))

解答

\frac{d}{d x} (\frac{x}{( x - 6 ) ^{2}})

\frac{- 6 - x}{( x - 6 ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{x}{( x - 6 ) ^{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} ( x - 6 ) ^{2} - \frac{d}{d x} ( ( x - 6 ) ^{2} ) x}{( ( x - 6 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x - 6)^{2}) = 2 (x - 6)

= \frac{1 \cdot ( x - 6 ) ^{2} - 2 ( x - 6 ) x}{( ( x - 6 ) ^{2} ) ^{2}}

化简

\frac{1 \cdot ( x - 6 ) ^{2} - 2 ( x - 6 ) x}{( ( x - 6 ) ^{2} ) ^{2}} : \frac{- 6 - x}{( x - 6 ) ^{3}}

= \frac{- 6 - x}{( x - 6 ) ^{3}}

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