(\partial)/(\partial θ)(r(θ)*cos(θ))

解

\frac{\partial}{\partial θ} (r (θ) \cdot cos (θ))

r (cos (θ) - θ sin (θ))

解答ステップ

\frac{\partial}{\partial θ} (r (θ) cos (θ))

r

を定数として扱う

定数を除去:

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

= r \frac{\partial}{\partial θ} (θ cos (θ))

積の法則を適用:

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

f = θ, g = cos (θ)

= r (\frac{\partial}{\partial θ} (θ) cos (θ) + \frac{\partial}{\partial θ} (cos (θ)) θ)

\frac{\partial}{\partial θ} (θ) = 1

\frac{\partial}{\partial θ} (cos (θ)) = - sin (θ)

= r (1 \cdot cos (θ) + (- sin (θ)) θ)

簡素化

= r (cos (θ) - θ sin (θ))