derivative of 1/(cos(2x))

解答

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

sec (2 x) tan (2 x) \cdot 2

求解步骤

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

化简

\frac{1}{cos ( 2 x )} : sec (2 x)

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

使用连锁律:

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

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

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

= sec (2 x) tan (2 x) \cdot 2