derivative (2x)/(x^2+1)

解答

导数

\frac{2 x}{x ^{2} + 1}

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

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分除法定则:

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

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

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

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

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

化简

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

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

x^{^{''}} + 3 x^{^{'}} + 2 x = e^{- t}

t an g e n t (3 x + 25)

\frac{\partial}{\partial x} (e^{2 x} cos (y))

x \to - 2 lim (3 x + 4)

\int x e^{5 x} d x