(\partial)/(\partial x)((z)(x+sin(x+z)))

解

\frac{\partial}{\partial x} ((z) (x + sin (x + z)))

z (1 + cos (x + z))

解答ステップ

\frac{\partial}{\partial x} ((z) (x + sin (x + z)))

z

を定数として扱う

定数を除去:

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

= z \frac{\partial}{\partial x} (x + sin (x + z))

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (sin (x + z)))

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (sin (x + z)) = cos (x + z)

= z (1 + cos (x + z))