(\partial)/(\partial x)((x^2y^2)^{1/3})

解

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

\frac{2 y ^{\frac{2}{3}}}{3 x ^{\frac{1}{3}}}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (x^{2} y^{2}) = 2 y^{2} x

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

簡素化

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

= \frac{2 y ^{\frac{2}{3}}}{3 x ^{\frac{1}{3}}}