derivative f(x)=sqrt(x)sec(x)

解

導関数

f (x) = x sec (x)

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

解答ステップ

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

積の法則を適用:

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

f = x, g = sec (x)

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

\frac{1}{2 x} sec (x) = \frac{sec ( x )}{2 x}

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