derivative of sqrt(5+xsec(x))

解

\frac{d}{d x} (5 + x sec (x))

\frac{x sec ( x ) tan ( x ) + sec ( x )}{2 5 + x sec ( x )}

解答ステップ

\frac{d}{d x} (5 + x sec (x))

連鎖法則を適用:

\frac{1}{2 5 + x sec ( x )} \frac{d}{d x} (5 + x sec (x))

= \frac{1}{2 5 + x sec ( x )} \frac{d}{d x} (5 + x sec (x))

\frac{d}{d x} (5 + x sec (x)) = x sec (x) tan (x) + sec (x)

= \frac{1}{2 5 + x sec ( x )} (x sec (x) tan (x) + sec (x))

簡素化

\frac{1}{2 5 + x sec ( x )} (x sec (x) tan (x) + sec (x)) : \frac{x sec ( x ) tan ( x ) + sec ( x )}{2 5 + x sec ( x )}

= \frac{x sec ( x ) tan ( x ) + sec ( x )}{2 5 + x sec ( x )}