derivative of (5x/(x^2+1))

解答

\frac{d}{d x} (\frac{5 x}{x ^{2} + 1})

\frac{5 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{5 x}{x ^{2} + 1})

将常数提出:

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

= 5 \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}}

= 5 \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

= 5 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}}

化简

5 \cdot \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}} : \frac{5 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

= \frac{5 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

n = 1 \sum \infty \frac{1}{n ^{2} + 3}

d er i v a t i v e f (x) = \frac{8 x ^{3} - 3 x + 2}{3 x - x ^{4}}

(cos (x^{2}) \cdot 2 x)^{^{'}}

\frac{\partial}{\partial x} (ln (x^{2} + y^{2} + x y))

\frac{\partial}{\partial y} (2 k y - 5 x)