(\partial ^2)/(\partial r\partial θ)(r(θ)*sin(θ))

解

\frac{\partial ^{2}}{\partial r \partial θ} (r (θ) \cdot sin (θ))

sin (θ) + θ cos (θ)

解答ステップ

\frac{\partial ^{2}}{\partial r \partial θ} (r (θ) sin (θ))

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

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

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

= sin (θ) + θ cos (θ)