(\partial)/(\partial x)(3cos(x)-sin(x)y)

解

\frac{\partial}{\partial x} (3 cos (x) - sin (x) y)

- 3 sin (x) - y cos (x)

解答ステップ

\frac{\partial}{\partial x} (3 cos (x) - sin (x) y)

y

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} (3 cos (x)) - \frac{\partial}{\partial x} (sin (x) y)

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

\frac{\partial}{\partial x} (sin (x) y) = y cos (x)

= - 3 sin (x) - y cos (x)