derivative f(x)=\sqrt[3]{x^7-4x}

解

導関数

f (x) = 3 x^{7} - 4 x

\frac{7 x ^{6} - 4}{3 ( x ^{7} - 4 x ) ^{\frac{2}{3}}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (x^{7} - 4 x) = 7 x^{6} - 4

= \frac{1}{3 ( x ^{7} - 4 x ) ^{\frac{2}{3}}} (7 x^{6} - 4)

簡素化

\frac{1}{3 ( x ^{7} - 4 x ) ^{\frac{2}{3}}} (7 x^{6} - 4) : \frac{7 x ^{6} - 4}{3 ( x ^{7} - 4 x ) ^{\frac{2}{3}}}

= \frac{7 x ^{6} - 4}{3 ( x ^{7} - 4 x ) ^{\frac{2}{3}}}