derivative of 7(\sqrt[3]{x}+(x^{1/3}/3))

解答

\frac{d}{d x} (7 (3 x + \frac{x ^{\frac{1}{3}}}{3}))

\frac{28}{9 x ^{\frac{2}{3}}}

求解步骤

\frac{d}{d x} (7 (3 x + \frac{x ^{\frac{1}{3}}}{3}))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (3 x + \frac{x ^{\frac{1}{3}}}{3})

使用微分加减法定则:

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

= 7 (\frac{d}{d x} (3 x) + \frac{d}{d x} (\frac{x ^{\frac{1}{3}}}{3}))

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

\frac{d}{d x} (\frac{x ^{\frac{1}{3}}}{3}) = \frac{1}{9 x ^{\frac{2}{3}}}

= 7 (\frac{1}{3 x ^{\frac{2}{3}}} + \frac{1}{9 x ^{\frac{2}{3}}})

化简

7 (\frac{1}{3 x ^{\frac{2}{3}}} + \frac{1}{9 x ^{\frac{2}{3}}}) : \frac{28}{9 x ^{\frac{2}{3}}}

= \frac{28}{9 x ^{\frac{2}{3}}}

\frac{\partial}{\partial x} (x + 3 lo g_{10} (x) - y^{2})

\int \frac{18}{x 1 + 2 x} d x

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

y^{^{''}} - 5 y^{^{'}} + 4 y = 0

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