derivative (10+sec(θ))sin(θ)

解答

导数

(10 + sec (θ)) sin (θ)

cos (θ) (10 + sec (θ)) + tan^{2} (θ)

求解步骤

\frac{d}{d θ} ((10 + sec (θ)) sin (θ))

使用微分乘法定则:

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

f = 10 + sec (θ), g = sin (θ)

= \frac{d}{d θ} (10 + sec (θ)) sin (θ) + \frac{d}{d θ} (sin (θ)) (10 + sec (θ))

\frac{d}{d θ} (10 + sec (θ)) = sec (θ) tan (θ)

\frac{d}{d θ} (sin (θ)) = cos (θ)

= sec (θ) tan (θ) sin (θ) + cos (θ) (10 + sec (θ))

化简

sec (θ) tan (θ) sin (θ) + cos (θ) (10 + sec (θ)) : cos (θ) (10 + sec (θ)) + tan^{2} (θ)

= cos (θ) (10 + sec (θ)) + tan^{2} (θ)

t a y l or \frac{1}{1 - x}, 8

\frac{d}{d x} (x^{2} ln (x^{5}))

f (x) = 6 e^{x}

\int \frac{5 x ^{2} - 6}{x ^{2} - 2 x - 8} d x

\frac{d}{d x} (sin^{2} (3 x + 2))