d/(dθ)(({r}(θ))(1-2θ))

解

\frac{d}{d θ} ((r (θ)) (1 - 2 θ))

\frac{d}{d θ} (r (θ)) (1 - 2 θ) - 2 r (θ)

解答ステップ

\frac{d}{d θ} ((r (θ)) (1 - 2 θ))

積の法則を適用:

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

f = r (θ), g = 1 - 2 θ

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

\frac{d}{d θ} (1 - 2 θ) = - 2

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

簡素化

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