derivative x/(x^2+81)

解答

导数

\frac{x}{x ^{2} + 81}

\frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x}{x ^{2} + 81})

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 ^{2} + 81 ) - \frac{d}{d x} ( x ^{2} + 81 ) x}{( x ^{2} + 81 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 81) = 2 x

= \frac{1 \cdot ( x ^{2} + 81 ) - 2 xx}{( x ^{2} + 81 ) ^{2}}

1 \cdot (x^{2} + 81) - 2 xx = - x^{2} + 81

= \frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

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

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