(\partial)/(\partial x)((y)(sin(z)x-x))

解

\frac{\partial}{\partial x} ((y) (sin (z) x - x))

y (sin (z) - 1)

解答ステップ

\frac{\partial}{\partial x} ((y) (sin (z) x - x))

y, z

を定数として扱う

定数を除去:

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

= y \frac{\partial}{\partial x} (sin (z) x - x)

和/差の法則を適用:

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

= y (\frac{\partial}{\partial x} (sin (z) x) - \frac{\partial}{\partial x} (x))

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

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

= y (sin (z) - 1)