derivative of \sqrt[7]{x}+2sqrt(x^7)

解

\frac{d}{d x} (7 x + 2 x^{7})

\frac{1 + 49 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

解答ステップ

\frac{d}{d x} (7 x + 2 x^{7})

和/差の法則を適用:

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

= \frac{d}{d x} (7 x) + \frac{d}{d x} (2 x^{7})

\frac{d}{d x} (7 x) = \frac{1}{7 x ^{\frac{6}{7}}}

\frac{d}{d x} (2 x^{7}) = 7 x^{\frac{5}{2}}

= \frac{1}{7 x ^{\frac{6}{7}}} + 7 x^{\frac{5}{2}}

簡素化

\frac{1}{7 x ^{\frac{6}{7}}} + 7 x^{\frac{5}{2}} : \frac{1 + 49 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

= \frac{1 + 49 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}