d/(dθ)(({x}(θ))(2(1-cos(θ))))

解答

\frac{d}{d θ} ((x (θ)) (2 (1 - cos (θ))))

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

求解步骤

\frac{d}{d θ} ((x (θ)) (2 (1 - cos (θ))))

将常数提出:

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

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

使用微分乘法定则:

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

f = x (θ), g = 1 - cos (θ)

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

\frac{d}{d θ} (1 - cos (θ)) = sin (θ)

= 2 (\frac{d}{d θ} (x (θ)) (1 - cos (θ)) + sin (θ) x (θ))

e x p an d x^{- \frac{1}{2}} + x^{- \frac{1}{2}}

e x p an d 2 + U (t - \frac{7}{2}) e^{- t} sin (π t)

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

e x p an d \frac{9 x ^{2} + 3 x + 2}{( x ^{2} - 9 ) x}

e x p an d \frac{5 x}{2 ( 2 x ^{2} + 1 )}