d/(dθ)(({r}(θ))(9-θ^3cos(θ)))

解答

\frac{d}{d θ} ((r (θ)) (9 - θ^{3} cos (θ)))

\frac{d}{d θ} (r (θ)) (9 - θ^{3} cos (θ)) + (θ^{3} sin (θ) - 3 θ^{2} cos (θ)) r (θ)

求解步骤

\frac{d}{d θ} ((r (θ)) (9 - θ^{3} cos (θ)))

使用微分乘法定则:

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

f = r (θ), g = 9 - θ^{3} cos (θ)

= \frac{d}{d θ} (r (θ)) (9 - θ^{3} cos (θ)) + \frac{d}{d θ} (9 - θ^{3} cos (θ)) r (θ)

\frac{d}{d θ} (9 - θ^{3} cos (θ)) = θ^{3} sin (θ) - 3 θ^{2} cos (θ)

= \frac{d}{d θ} (r (θ)) (9 - θ^{3} cos (θ)) + (θ^{3} sin (θ) - 3 θ^{2} cos (θ)) r (θ)

e x p an d 1 + \frac{( k \cdot ( s ^{2} - 2 s + 2 ) )}{s ( s + 1 ) ( s + 2 )}

s im pl i f y - (\frac{9}{13} lo g_{2} (\frac{9}{13}) + \frac{4}{13} lo g_{2} (\frac{4}{13}))

e x p an d ln (20) (e^{\frac{x}{52}} - 1)

e x p an d 2 t^{4} e^{- 2 t} + [U^{4} (t) (t - 3)]

e x p an d sin ((4 n + 3) \cdot 9 0^{\circ})