derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2})

解

\frac{d}{d x} (3 27 x^{2} - \frac{1}{3 27 x ^{2}})

\frac{2}{x ^{\frac{1}{3}}} + \frac{2}{9 x ^{\frac{5}{3}}}

解答ステップ

\frac{d}{d x} (3 27 x^{2} - \frac{1}{3 27 x ^{2}})

和/差の法則を適用:

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

= \frac{d}{d x} (3 27 x^{2}) - \frac{d}{d x} (\frac{1}{3 27 x ^{2}})

\frac{d}{d x} (3 27 x^{2}) = \frac{2}{x ^{\frac{1}{3}}}

\frac{d}{d x} (\frac{1}{3 27 x ^{2}}) = - \frac{2}{9 x ^{\frac{5}{3}}}

= \frac{2}{x ^{\frac{1}{3}}} - (- \frac{2}{9 x ^{\frac{5}{3}}})

簡素化

= \frac{2}{x ^{\frac{1}{3}}} + \frac{2}{9 x ^{\frac{5}{3}}}