derivative (8x^2+6x+2)/(sqrt(x))

解答

导数

\frac{8 x ^{2} + 6 x + 2}{x}

\frac{12 x ^{2} + 3 x - 1}{x x}

求解步骤

\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 2}{x})

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} ( 8 x ^{2} + 6 x + 2 ) x - \frac{d}{d x} ( x ) ( 8 x ^{2} + 6 x + 2 )}{( x ) ^{2}}

\frac{d}{d x} (8 x^{2} + 6 x + 2) = 16 x + 6

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

= \frac{( 16 x + 6 ) x - \frac{1}{2 x} ( 8 x ^{2} + 6 x + 2 )}{( x ) ^{2}}

化简

\frac{( 16 x + 6 ) x - \frac{1}{2 x} ( 8 x ^{2} + 6 x + 2 )}{( x ) ^{2}} : \frac{12 x ^{2} + 3 x - 1}{x x}

= \frac{12 x ^{2} + 3 x - 1}{x x}

d er i v a t i v e y = (arctan (4 x))^{2}

\int \frac{x - 2}{x ^{2}} d x

\frac{d}{d x} (x e^{x y})

\frac{d}{d x} (8 x^{- 3})

d er i v a t i v e \frac{x}{11} - \frac{11}{x}