derivative (sin(4t))/(cos(6t))

解

導関数

\frac{sin ( 4 t )}{cos ( 6 t )}

cos (4 t) \cdot 4 sec (6 t) + sec (6 t) tan (6 t) \cdot 6 sin (4 t)

解答ステップ

\frac{d}{d t} (\frac{sin ( 4 t )}{cos ( 6 t )})

簡素化

\frac{sin ( 4 t )}{cos ( 6 t )} : sin (4 t) sec (6 t)

= \frac{d}{d t} (sin (4 t) sec (6 t))

積の法則を適用:

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

f = sin (4 t), g = sec (6 t)

= \frac{d}{d t} (sin (4 t)) sec (6 t) + \frac{d}{d t} (sec (6 t)) sin (4 t)

\frac{d}{d t} (sin (4 t)) = cos (4 t) \cdot 4

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

= cos (4 t) \cdot 4 sec (6 t) + sec (6 t) tan (6 t) \cdot 6 sin (4 t)