(\partial)/(\partial x)(3sin(2x)cos(6y))

解

\frac{\partial}{\partial x} (3 sin (2 x) cos (6 y))

6 cos (2 x) cos (6 y)

解答ステップ

\frac{\partial}{\partial x} (3 sin (2 x) cos (6 y))

y

を定数として扱う

定数を除去:

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

= 3 cos (6 y) \frac{\partial}{\partial x} (sin (2 x))

連鎖法則を適用:

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

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

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

= 3 cos (6 y) cos (2 x) \cdot 2

簡素化

= 6 cos (2 x) cos (6 y)