d/(dθ)(4sin^2(θ)cos(θ))

解

\frac{d}{d θ} (4 sin^{2} (θ) cos (θ))

4 (sin (2 θ) cos (θ) - sin^{3} (θ))

解答ステップ

\frac{d}{d θ} (4 sin^{2} (θ) cos (θ))

定数を除去:

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

= 4 \frac{d}{d θ} (sin^{2} (θ) cos (θ))

積の法則を適用:

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

f = sin^{2} (θ), g = cos (θ)

= 4 (\frac{d}{d θ} (sin^{2} (θ)) cos (θ) + \frac{d}{d θ} (cos (θ)) sin^{2} (θ))

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

= 4 (sin (2 θ) cos (θ) + (- sin (θ)) sin^{2} (θ))

簡素化

4 (sin (2 θ) cos (θ) + (- sin (θ)) sin^{2} (θ)) : 4 (sin (2 θ) cos (θ) - sin^{3} (θ))

= 4 (sin (2 θ) cos (θ) - sin^{3} (θ))