(\partial)/(\partial x)(-6sin(2x+y))

解

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

- 12 cos (2 x + y)

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

cos (2 x + y) \frac{\partial}{\partial x} (2 x + y)

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

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

= - 6 cos (2 x + y) \cdot 2

簡素化

= - 12 cos (2 x + y)