derivative g(x)=(sin(8x))/(cos(x))

解

導関数

g (x) = \frac{sin ( 8 x )}{cos ( x )}

cos (8 x) \cdot 8 sec (x) + sec (x) tan (x) sin (8 x)

解答ステップ

\frac{d}{d x} (\frac{sin ( 8 x )}{cos ( x )})

簡素化

\frac{sin ( 8 x )}{cos ( x )} : sin (8 x) sec (x)

= \frac{d}{d x} (sin (8 x) sec (x))

積の法則を適用:

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

f = sin (8 x), g = sec (x)

= \frac{d}{d x} (sin (8 x)) sec (x) + \frac{d}{d x} (sec (x)) sin (8 x)

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

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

= cos (8 x) \cdot 8 sec (x) + sec (x) tan (x) sin (8 x)