derivative f(x)=(x^2+8x+3)/(sqrt(x))

解答

导数

f (x) = \frac{x ^{2} + 8 x + 3}{x}

\frac{3 x ^{2} + 8 x - 3}{2 x x}

求解步骤

\frac{d}{d x} (\frac{x ^{2} + 8 x + 3}{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} ( x ^{2} + 8 x + 3 ) x - \frac{d}{d x} ( x ) ( x ^{2} + 8 x + 3 )}{( x ) ^{2}}

\frac{d}{d x} (x^{2} + 8 x + 3) = 2 x + 8

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

= \frac{( 2 x + 8 ) x - \frac{1}{2 x} ( x ^{2} + 8 x + 3 )}{( x ) ^{2}}

化简

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

= \frac{3 x ^{2} + 8 x - 3}{2 x x}

x \to \infty lim (\frac{x ^{2} + 2 x + 5}{e ^{3 x}})

\frac{d}{d x} (e^{x} cos (x) + e^{x} sin (x))

\int \frac{sin ^{2} ( 3 x )}{cos ( 3 x )} d x

\int \frac{1}{( 169 - x ^{2} ) ^{\frac{3}{2}}} d x

t a y l or 1 - x^{3}