derivative of 4sqrt(x)+8x^{3/8}

解

\frac{d}{d x} (4 x + 8 x^{\frac{3}{8}})

\frac{2}{x ^{\frac{1}{2}}} + \frac{3}{x ^{\frac{5}{8}}}

解答ステップ

\frac{d}{d x} (4 x + 8 x^{\frac{3}{8}})

和/差の法則を適用:

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

= \frac{d}{d x} (4 x) + \frac{d}{d x} (8 x^{\frac{3}{8}})

\frac{d}{d x} (4 x) = \frac{2}{x ^{\frac{1}{2}}}

\frac{d}{d x} (8 x^{\frac{3}{8}}) = \frac{3}{x ^{\frac{5}{8}}}

= \frac{2}{x ^{\frac{1}{2}}} + \frac{3}{x ^{\frac{5}{8}}}