**Derivative Of Sec 2x**

Derived from the second 2 (x)?

2 * sec 2 (x) * corresponds to tan (x), but why is the 2 part missing? The derivative of sin der 2 (x) = 2sinxcosx, so I think the part will be lost in the derivative of 2 seconds 2 (x).

Coming from seconds.

Here you need to apply the principle of chain. The derivative of seconds (x) is seconds; 2 (x) * tan (x)

So the reason 2 does not disappear is that the second (x) is the securit (x), while the derivative of sin (x) is only cos (x).

Once the derivative is formed, the result is 2 second (x) factors:

(d / dx) sec 2 (x) = 2 * sec (x) * (d / dx) sec (x) = 2 * sec (x) * sec (x) * tan (x) = 2 * sec 2 (x) * chocolate (x),

Using reality (d / dx) seconds (x) = seconds (x) * tan (x).

To see (d / dx) sec (x) = sec (x) * tan (x), remember sec (x) = 1 / cos (x)

(d / dx) 1 / cos (x) = (d / dx) cos 1 (x) = 1 * cos 2 * (d / dx) cos (x) = 1 * cos 2 * 1 * sin ( x) =

sin (x) / cos 2 (x) = [sin (x) / cos (x)] * 1 / cos (x) = tan (x) * sec (x).