d/(dθ)(({x}(θ))(2(1-cos(θ))))

解

\frac{d}{d θ} ((x (θ)) (2 (1 - cos (θ))))

2 (\frac{d}{d θ} (x (θ)) (1 - cos (θ)) + sin (θ) x (θ))

解答ステップ

\frac{d}{d θ} ((x (θ)) (2 (1 - cos (θ))))

定数を除去:

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

= 2 \frac{d}{d θ} (x (θ) (1 - cos (θ)))

積の法則を適用:

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

f = x (θ), g = 1 - cos (θ)

= 2 (\frac{d}{d θ} (x (θ)) (1 - cos (θ)) + \frac{d}{d θ} (1 - cos (θ)) x (θ))

\frac{d}{d θ} (1 - cos (θ)) = sin (θ)

= 2 (\frac{d}{d θ} (x (θ)) (1 - cos (θ)) + sin (θ) x (θ))