derivative of (x^3-2xsqrt(x)/x)

解答

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

2 x - \frac{1}{x}

求解步骤

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

化简

\frac{x ^{3} - 2 x x}{x} : x^{2} - 2 x

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

使用微分加减法定则:

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

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

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

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

= 2 x - \frac{1}{x}

s l o p e (0, - 9), (7, 6)

t an g e n t f (x) = x (x^{2} - 4 x + 5)^{5}, at x = 2

x \cdot y^{^{'}} = 2 y + e^{x} \cdot x^{3}

x \to - \frac{1}{2} lim (\frac{7}{2 x + 1})

a re a - x^{2} + 2 x, 3 x^{3} - x^{2} - 10 x