(\partial)/(\partial x)(5xy(9-x-y))

解

\frac{\partial}{\partial x} (5 x y (9 - x - y))

5 y (- 2 x - y + 9)

解答ステップ

\frac{\partial}{\partial x} (5 x y (9 - x - y))

y

を定数として扱う

定数を除去:

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

= 5 y \frac{\partial}{\partial x} (x (9 - x - y))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 9 - x - y

= 5 y (\frac{\partial}{\partial x} (x) (9 - x - y) + \frac{\partial}{\partial x} (9 - x - y) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (9 - x - y) = - 1

= 5 y (1 \cdot (9 - x - y) + (- 1) x)

簡素化

5 y (1 \cdot (9 - x - y) + (- 1) x) : 5 y (- 2 x - y + 9)

= 5 y (- 2 x - y + 9)