(\partial)/(\partial x)(-ae^{kz}wsin(kx-wt))

解

\frac{\partial}{\partial x} (- a e^{k z} w sin (k x - wt))

- a e^{k z} w cos (k x - wt) k

解答ステップ

\frac{\partial}{\partial x} (- a e^{k z} w sin (k x - wt))

a, k, z, w, t

を定数として扱う

定数を除去:

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

= - a e^{k z} w \frac{\partial}{\partial x} (sin (k x - wt))

連鎖法則を適用:

cos (k x - wt) \frac{\partial}{\partial x} (k x - wt)

= cos (k x - wt) \frac{\partial}{\partial x} (k x - wt)

\frac{\partial}{\partial x} (k x - wt) = k

= - a e^{k z} w cos (k x - wt) k