(\partial)/(\partial x)(sin(x)*cos(x))

解

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

cos (2 x)

解答ステップ

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

積の法則を適用:

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

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

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

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

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

= cos (x) cos (x) + (- sin (x)) sin (x)

簡素化

cos (x) cos (x) + (- sin (x)) sin (x) : cos (2 x)

= cos (2 x)