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

解答

导数

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

\frac{2 x ^{3} - 5 x ^{2} - 4 x - 3}{( x - 2 ) ^{2}}

求解步骤

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

使用微分除法定则:

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

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

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

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

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

化简

\frac{( 3 x ^{2} + 2 x + 1 ) ( x - 2 ) - 1 \cdot ( x + 1 ) ( x ^{2} + 1 )}{( x - 2 ) ^{2}} : \frac{2 x ^{3} - 5 x ^{2} - 4 x - 3}{( x - 2 ) ^{2}}

= \frac{2 x ^{3} - 5 x ^{2} - 4 x - 3}{( x - 2 ) ^{2}}

\int_{- 1}^{1} (6 x^{5} + 3) d x

d er i v a t i v e y = \frac{9 x}{e ^{x}}

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

\frac{d y}{d x} - 3 y = 2

\int \frac{1}{( x ^{2} - 9 )} d x