derivative \sqrt[5]{2x^3+8x}

解

導関数

5 2 x^{3} + 8 x

\frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

解答ステップ

\frac{d}{d x} (5 2 x^{3} + 8 x)

連鎖法則を適用:

\frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} \frac{d}{d x} (2 x^{3} + 8 x)

= \frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} \frac{d}{d x} (2 x^{3} + 8 x)

\frac{d}{d x} (2 x^{3} + 8 x) = 6 x^{2} + 8

= \frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} (6 x^{2} + 8)

簡素化

\frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} (6 x^{2} + 8) : \frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

= \frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}