derivative of \sqrt[4]{x^5-x^3-2}

解

\frac{d}{d x} (4 x^{5} - x^{3} - 2)

\frac{5 x ^{4} - 3 x ^{2}}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}}

解答ステップ

\frac{d}{d x} (4 x^{5} - x^{3} - 2)

連鎖法則を適用:

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

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

\frac{d}{d x} (x^{5} - x^{3} - 2) = 5 x^{4} - 3 x^{2}

= \frac{1}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}} (5 x^{4} - 3 x^{2})

簡素化

\frac{1}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}} (5 x^{4} - 3 x^{2}) : \frac{5 x ^{4} - 3 x ^{2}}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}}

= \frac{5 x ^{4} - 3 x ^{2}}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}}