derivative of (sin(5x)/(cos(6x)))

解

\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

cos (5 x) \cdot 5 sec (6 x) + sec (6 x) tan (6 x) \cdot 6 sin (5 x)

解答ステップ

\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

簡素化

\frac{sin ( 5 x )}{cos ( 6 x )} : sin (5 x) sec (6 x)

= \frac{d}{d x} (sin (5 x) sec (6 x))

積の法則を適用:

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

f = sin (5 x), g = sec (6 x)

= \frac{d}{d x} (sin (5 x)) sec (6 x) + \frac{d}{d x} (sec (6 x)) sin (5 x)

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

\frac{d}{d x} (sec (6 x)) = sec (6 x) tan (6 x) \cdot 6

= cos (5 x) \cdot 5 sec (6 x) + sec (6 x) tan (6 x) \cdot 6 sin (5 x)