(\partial)/(\partial x)(y(x^2+y)^6)

解

\frac{\partial}{\partial x} (y (x^{2} + y)^{6})

12 y x (x^{2} + y)^{5}

解答ステップ

\frac{\partial}{\partial x} (y (x^{2} + y)^{6})

y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} ((x^{2} + y)^{6})

連鎖法則を適用:

6 (x^{2} + y)^{5} \frac{\partial}{\partial x} (x^{2} + y)

= 6 (x^{2} + y)^{5} \frac{\partial}{\partial x} (x^{2} + y)

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

= y \cdot 6 (x^{2} + y)^{5} \cdot 2 x

簡素化

= 12 y x (x^{2} + y)^{5}