derivative of (sin(x+cos(x))sec(x)dx)

解

\frac{d}{d x} ((sin (x) + cos (x)) sec (x) d x)

d ((cos (x) - sin (x)) sec (x) x + (x sec (x) tan (x) + sec (x)) (sin (x) + cos (x)))

解答ステップ

\frac{d}{d x} ((sin (x) + cos (x)) sec (x) d x)

d

を定数として扱う

定数を除去:

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

= d \frac{d}{d x} ((sin (x) + cos (x)) sec (x) x)

積の法則を適用:

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

f = sin (x) + cos (x), g = sec (x) x

= d (\frac{d}{d x} (sin (x) + cos (x)) sec (x) x + \frac{d}{d x} (sec (x) x) (sin (x) + cos (x)))

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

\frac{d}{d x} (sec (x) x) = x sec (x) tan (x) + sec (x)

= d ((cos (x) - sin (x)) sec (x) x + (x sec (x) tan (x) + sec (x)) (sin (x) + cos (x)))