d/(dθ)(({r}(θ))(1+sec(θ))sin(θ))

解答

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

\frac{d}{d θ} (r (θ)) (1 + sec (θ)) sin (θ) + (cos (θ) + sec^{2} (θ)) r (θ)

求解步骤

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

使用微分乘法定则:

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

f = r (θ), g = (1 + sec (θ)) sin (θ)

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

\frac{d}{d θ} ((1 + sec (θ)) sin (θ)) = cos (θ) + sec^{2} (θ)

= \frac{d}{d θ} (r (θ)) (1 + sec (θ)) sin (θ) + (cos (θ) + sec^{2} (θ)) r (θ)

e x p an d \frac{( 3 x ^{2} + 10 y ^{4} ) ^{2}}{16}

e x p an d (sin (2 θ) + 2 sin (θ)) (1 - cos (θ))

e x p an d x (x - 10 x)

e x p an d \frac{( sin ( x ) e ^{x} ) - ( e ^{x} \cdot cos ( x ) )}{( sin ( x ) ) ^{2}}

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