derivative of 4\sqrt[3]{x^7}-1/(x^2+2x)

解

\frac{d}{d x} (4 3 x^{7} - \frac{1}{x ^{2}} + 2 x)

\frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2

解答ステップ

\frac{d}{d x} (4 3 x^{7} - \frac{1}{x ^{2}} + 2 x)

和/差の法則を適用:

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

= \frac{d}{d x} (4 3 x^{7}) - \frac{d}{d x} (\frac{1}{x ^{2}}) + \frac{d}{d x} (2 x)

\frac{d}{d x} (4 3 x^{7}) = \frac{28 x ^{\frac{4}{3}}}{3}

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

\frac{d}{d x} (2 x) = 2

= \frac{28 x ^{\frac{4}{3}}}{3} - (- \frac{2}{x ^{3}}) + 2

簡素化

\frac{28 x ^{\frac{4}{3}}}{3} - (- \frac{2}{x ^{3}}) + 2 : \frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2

= \frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2