derivative of 5sec(2x)

解答

\frac{d}{d x} (5 sec (2 x))

10 sec (2 x) tan (2 x)

求解步骤

\frac{d}{d x} (5 sec (2 x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \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

= 5 sec (2 x) tan (2 x) \cdot 2

化简

= 10 sec (2 x) tan (2 x)

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