derivative \sqrt[5]{x}+4sqrt(x^5)

解

導関数

5 x + 4 x^{5}

\frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

解答ステップ

\frac{d}{d x} (5 x + 4 x^{5})

和/差の法則を適用:

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

= \frac{d}{d x} (5 x) + \frac{d}{d x} (4 x^{5})

\frac{d}{d x} (5 x) = \frac{1}{5 x ^{\frac{4}{5}}}

\frac{d}{d x} (4 x^{5}) = 10 x^{\frac{3}{2}}

= \frac{1}{5 x ^{\frac{4}{5}}} + 10 x^{\frac{3}{2}}

簡素化

\frac{1}{5 x ^{\frac{4}{5}}} + 10 x^{\frac{3}{2}} : \frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

= \frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}