(\partial)/(\partial x)(4cos^3(kx-wt)-3cos(kx-wt))

解

\frac{\partial}{\partial x} (4 cos^{3} (k x - wt) - 3 cos (k x - wt))

- 12 k cos^{2} (k x - wt) sin (k x - wt) + 3 k sin (k x - wt)

解答ステップ

\frac{\partial}{\partial x} (4 cos^{3} (k x - wt) - 3 cos (k x - wt))

k, w, t

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (4 cos^{3} (k x - wt)) - \frac{\partial}{\partial x} (3 cos (k x - wt))

\frac{\partial}{\partial x} (4 cos^{3} (k x - wt)) = - 12 k cos^{2} (k x - wt) sin (k x - wt)

\frac{\partial}{\partial x} (3 cos (k x - wt)) = - 3 k sin (k x - wt)

= - 12 k cos^{2} (k x - wt) sin (k x - wt) - (- 3 k sin (k x - wt))

簡素化

= - 12 k cos^{2} (k x - wt) sin (k x - wt) + 3 k sin (k x - wt)