(\partial)/(\partial x)(\sqrt[3]{(x+1)^2})

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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