(\partial)/(\partial v)((u^2v-v^3)^5)

解

\frac{\partial}{\partial v} ((u^{2} v - v^{3})^{5})

5 (u^{2} v - v^{3})^{4} (u^{2} - 3 v^{2})

解答ステップ

\frac{\partial}{\partial v} ((u^{2} v - v^{3})^{5})

u

を定数として扱う

連鎖法則を適用:

5 (u^{2} v - v^{3})^{4} \frac{\partial}{\partial v} (u^{2} v - v^{3})

= 5 (u^{2} v - v^{3})^{4} \frac{\partial}{\partial v} (u^{2} v - v^{3})

\frac{\partial}{\partial v} (u^{2} v - v^{3}) = u^{2} - 3 v^{2}

= 5 (u^{2} v - v^{3})^{4} (u^{2} - 3 v^{2})