(\partial)/(\partial x)((x^2+5xy-2y)^8)

解

\frac{\partial}{\partial x} ((x^{2} + 5 x y - 2 y)^{8})

8 (x^{2} + 5 x y - 2 y)^{7} (2 x + 5 y)

解答ステップ

\frac{\partial}{\partial x} ((x^{2} + 5 x y - 2 y)^{8})

y

を定数として扱う

連鎖法則を適用:

8 (x^{2} + 5 x y - 2 y)^{7} \frac{\partial}{\partial x} (x^{2} + 5 x y - 2 y)

= 8 (x^{2} + 5 x y - 2 y)^{7} \frac{\partial}{\partial x} (x^{2} + 5 x y - 2 y)

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

= 8 (x^{2} + 5 x y - 2 y)^{7} (2 x + 5 y)