(\partial)/(\partial x)((1+2xy^2)^3)

解

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

6 y^{2} (1 + 2 x y^{2})^{2}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

= 6 y^{2} (1 + 2 x y^{2})^{2}