derivative of \sqrt[3]{x^2}+2sqrt(x^5)

解

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

\frac{2 + 15 x ^{\frac{11}{6}}}{3 x ^{\frac{1}{3}}}

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (3 x^{2}) = \frac{2}{3 x ^{\frac{1}{3}}}

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

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

簡素化

\frac{2}{3 x ^{\frac{1}{3}}} + 5 x^{\frac{3}{2}} : \frac{2 + 15 x ^{\frac{11}{6}}}{3 x ^{\frac{1}{3}}}

= \frac{2 + 15 x ^{\frac{11}{6}}}{3 x ^{\frac{1}{3}}}