d/(dθ)(({p}(θ))(2sin(2θ)))

解

\frac{d}{d θ} ((p (θ)) (2 sin (2 θ)))

2 (\frac{d}{d θ} (p (θ)) sin (2 θ) + cos (2 θ) \cdot 2 p (θ))

解答ステップ

\frac{d}{d θ} ((p (θ)) (2 sin (2 θ)))

定数を除去:

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

= 2 \frac{d}{d θ} (p (θ) sin (2 θ))

積の法則を適用:

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

f = p (θ), g = sin (2 θ)

= 2 (\frac{d}{d θ} (p (θ)) sin (2 θ) + \frac{d}{d θ} (sin (2 θ)) p (θ))

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

= 2 (\frac{d}{d θ} (p (θ)) sin (2 θ) + cos (2 θ) \cdot 2 p (θ))