d/(da)(2sin^2(a)cos^2(a))

解

\frac{d}{d a} (2 sin^{2} (a) cos^{2} (a))

2 sin (2 a) cos (2 a)

解答ステップ

\frac{d}{d a} (2 sin^{2} (a) cos^{2} (a))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d a} (sin^{2} (a) cos^{2} (a))

積の法則を適用:

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

f = sin^{2} (a), g = cos^{2} (a)

= 2 (\frac{d}{d a} (sin^{2} (a)) cos^{2} (a) + \frac{d}{d a} (cos^{2} (a)) sin^{2} (a))

\frac{d}{d a} (sin^{2} (a)) = sin (2 a)

\frac{d}{d a} (cos^{2} (a)) = - sin (2 a)

= 2 (sin (2 a) cos^{2} (a) + (- sin (2 a)) sin^{2} (a))

簡素化

2 (sin (2 a) cos^{2} (a) + (- sin (2 a)) sin^{2} (a)) : 2 sin (2 a) cos (2 a)

= 2 sin (2 a) cos (2 a)