derivative (10+sec(θ))sin(θ)

解

導関数

(10 + sec (θ)) sin (θ)

cos (θ) (10 + sec (θ)) + tan^{2} (θ)

解答ステップ

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

積の法則を適用:

(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))

簡素化

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)