derivative x^8+x^{1/8}

解

導関数

x^{8} + x^{\frac{1}{8}}

\frac{1 + 64 x ^{\frac{63}{8}}}{8 x ^{\frac{7}{8}}}

解答ステップ

\frac{d}{d x} (x^{8} + x^{\frac{1}{8}})

和/差の法則を適用:

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

= \frac{d}{d x} (x^{8}) + \frac{d}{d x} (x^{\frac{1}{8}})

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} (x^{\frac{1}{8}}) = \frac{1}{8 x ^{\frac{7}{8}}}

= 8 x^{7} + \frac{1}{8 x ^{\frac{7}{8}}}

簡素化

8 x^{7} + \frac{1}{8 x ^{\frac{7}{8}}} : \frac{1 + 64 x ^{\frac{63}{8}}}{8 x ^{\frac{7}{8}}}

= \frac{1 + 64 x ^{\frac{63}{8}}}{8 x ^{\frac{7}{8}}}