derivative of ln(x+\sqrt[5]{x^3})

解答

\frac{d}{d x} (ln (x) + 5 x^{3})

\frac{5 x ^{\frac{2}{5}} + 3 x}{5 x ^{\frac{7}{5}}}

求解步骤

\frac{d}{d x} (ln (x) + 5 x^{3})

使用微分加减法定则:

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

= \frac{d}{d x} (ln (x)) + \frac{d}{d x} (5 x^{3})

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

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

= \frac{1}{x} + \frac{3}{5 x ^{\frac{2}{5}}}

化简

\frac{1}{x} + \frac{3}{5 x ^{\frac{2}{5}}} : \frac{5 x ^{\frac{2}{5}} + 3 x}{5 x ^{\frac{7}{5}}}

= \frac{5 x ^{\frac{2}{5}} + 3 x}{5 x ^{\frac{7}{5}}}

x \to 0 lim (a^{x} + a^{- x})

\int (3 x + 4)^{6} d x

y^{^{'}} + e^{x} y = 19 e^{x}

\frac{\partial}{\partial w} ((y - w (x + x^{2}))^{2})

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