derivative (sec(x))/(x^2)

解

導関数

\frac{sec ( x )}{x ^{2}}

\frac{sec ( x ) ( x tan ( x ) - 2 )}{x ^{3}}

解答ステップ

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

簡素化

\frac{sec ( x ) tan ( x ) x ^{2} - 2 x sec ( x )}{( x ^{2} ) ^{2}} : \frac{sec ( x ) ( x tan ( x ) - 2 )}{x ^{3}}

= \frac{sec ( x ) ( x tan ( x ) - 2 )}{x ^{3}}