derivative f(x)=sin(x)cos(x)

解

導関数

f (x) = sin (x) cos (x)

cos (2 x)

解答ステップ

\frac{d}{d 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{d}{d x} (sin (x)) cos (x) + \frac{d}{d x} (cos (x)) sin (x)

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

\frac{d}{d 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)