(\partial)/(\partial x)(cos(x)sin(x)-xy)

解

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

cos (2 x) - y

解答ステップ

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

\frac{\partial}{\partial x} (cos (x) sin (x)) = cos (2 x)

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

= cos (2 x) - y