(\partial)/(\partial z)(e^{3x+4y}cos(5z))

解

\frac{\partial}{\partial z} (e^{3 x + 4 y} cos (5 z))

- 5 e^{3 x + 4 y} sin (5 z)

解答ステップ

\frac{\partial}{\partial z} (e^{3 x + 4 y} cos (5 z))

x, y

を定数として扱う

定数を除去:

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

= e^{3 x + 4 y} \frac{\partial}{\partial z} (cos (5 z))

連鎖法則を適用:

- sin (5 z) \frac{\partial}{\partial z} (5 z)

= - sin (5 z) \frac{\partial}{\partial z} (5 z)

\frac{\partial}{\partial z} (5 z) = 5

= e^{3 x + 4 y} (- sin (5 z) \cdot 5)

簡素化

= - 5 e^{3 x + 4 y} sin (5 z)