(\partial)/(\partial x)(e^{8x}cos(5y))

解

\frac{\partial}{\partial x} (e^{8 x} cos (5 y))

cos (5 y) e^{8 x} \cdot 8

解答ステップ

\frac{\partial}{\partial x} (e^{8 x} cos (5 y))

y

を定数として扱う

定数を除去:

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

= cos (5 y) \frac{\partial}{\partial x} (e^{8 x})

連鎖法則を適用:

e^{8 x} \frac{\partial}{\partial x} (8 x)

= e^{8 x} \frac{\partial}{\partial x} (8 x)

\frac{\partial}{\partial x} (8 x) = 8

= cos (5 y) e^{8 x} \cdot 8