derivative 4/(cos(x))+1/(tan(x))

解

導関数

\frac{4}{cos ( x )} + \frac{1}{tan ( x )}

4 sec (x) tan (x) - csc^{2} (x)

解答ステップ

\frac{d}{d x} (\frac{4}{cos ( x )} + \frac{1}{tan ( x )})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{4}{cos ( x )}) + \frac{d}{d x} (\frac{1}{tan ( x )})

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

\frac{d}{d x} (\frac{1}{tan ( x )}) = - csc^{2} (x)

= 4 sec (x) tan (x) - csc^{2} (x)