(\partial)/(\partial x)(-6e^{6y}sin(6x))

解

\frac{\partial}{\partial x} (- 6 e^{6 y} sin (6 x))

- 36 e^{6 y} cos (6 x)

解答ステップ

\frac{\partial}{\partial x} (- 6 e^{6 y} sin (6 x))

y

を定数として扱う

定数を除去:

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

= - 6 e^{6 y} \frac{\partial}{\partial x} (sin (6 x))

連鎖法則を適用:

cos (6 x) \frac{\partial}{\partial x} (6 x)

= cos (6 x) \frac{\partial}{\partial x} (6 x)

\frac{\partial}{\partial x} (6 x) = 6

= - 6 e^{6 y} cos (6 x) \cdot 6

簡素化

= - 36 e^{6 y} cos (6 x)