derivative of 2x+(x^2-x/(x^3+x+1))

解答

\frac{d}{d x} (2 x + \frac{x ^{2} - x}{x ^{3} + x + 1})

2 + \frac{- x ^{4} + 2 x ^{3} + x ^{2} + 2 x - 1}{( x ^{3} + x + 1 ) ^{2}}

求解步骤

\frac{d}{d x} (2 x + \frac{x ^{2} - x}{x ^{3} + x + 1})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (\frac{x ^{2} - x}{x ^{3} + x + 1}) = \frac{- x ^{4} + 2 x ^{3} + x ^{2} + 2 x - 1}{( x ^{3} + x + 1 ) ^{2}}

= 2 + \frac{- x ^{4} + 2 x ^{3} + x ^{2} + 2 x - 1}{( x ^{3} + x + 1 ) ^{2}}

t a y l or sin (4 x) cos (2 x)

\int \frac{1.2 x}{x ^{2} x ^{4} - 9} d x

(\frac{sin ( x )}{1 + x})^{^{'}}

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (0) = - 2, y^{^{'}} (0) = - 4

(- x + 2) \cdot y^{^{'}} - y = e^{- 2 x}