d/(dθ)({r}(θ)(1-cos(θ)))

解答

\frac{d}{d θ} (r (θ) (1 - cos (θ)))

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

求解步骤

\frac{d}{d θ} (r (θ) (1 - cos (θ)))

使用微分乘法定则:

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

f = r (θ), g = 1 - cos (θ)

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

\frac{d}{d θ} (1 - cos (θ)) = sin (θ)

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