derivative tan(x)-1sec(x)

解

導関数

tan (x) - 1 sec (x)

\frac{1}{1 + sin ( x )}

解答ステップ

\frac{d}{d x} (tan (x) - 1 \cdot sec (x))

簡素化

tan (x) - 1 \cdot sec (x) : tan (x) - sec (x)

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= sec^{2} (x) - sec (x) tan (x)

簡素化

sec^{2} (x) - sec (x) tan (x) : \frac{1}{1 + sin ( x )}

= \frac{1}{1 + sin ( x )}