(\partial)/(\partial x)(xcos(x)sin(x))

解

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

cos (x) sin (x) + x cos (2 x)

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (x) sin (x)

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

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

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

= 1 \cdot cos (x) sin (x) + cos (2 x) x

簡素化

= cos (x) sin (x) + x cos (2 x)