derivative x/(x^2+3)

解答

导数

\frac{x}{x ^{2} + 3}

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

求解步骤

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

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

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

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

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

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

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

\int cos^{2} (x s i) n^{3} x d x

t an g e n t e^{- 2 t}, at t = 0

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

x \to - 1 lim (2 x^{2} + 6 x - 1)

x \to 2 lim (\frac{5}{∣ 2 - x ∣})