derivative of 4asec(xtan(x))

解

\frac{d}{d x} (4 a sec (x) tan (x))

4 a (- sec (x) + 2 sec^{3} (x))

解答ステップ

\frac{d}{d x} (4 a sec (x) tan (x))

定数を除去:

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

= 4 a \frac{d}{d x} (sec (x) tan (x))

積の法則を適用:

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

f = sec (x), g = tan (x)

= 4 a (\frac{d}{d x} (sec (x)) tan (x) + \frac{d}{d x} (tan (x)) sec (x))

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= 4 a (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x))

簡素化

4 a (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)) : 4 a (- sec (x) + 2 sec^{3} (x))

= 4 a (- sec (x) + 2 sec^{3} (x))