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

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

= \frac{1}{3 ( ( x ^{2} + 1 ) ^{2} ) ^{\frac{2}{3}}} \cdot 4 x (x^{2} + 1)

簡素化

\frac{1}{3 ( ( x ^{2} + 1 ) ^{2} ) ^{\frac{2}{3}}} \cdot 4 x (x^{2} + 1) : \frac{4 x}{3 ( x ^{2} + 1 ) ^{\frac{1}{3}}}

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