Question

What is Derivatives of `y=sec(x)` ?

Answer 1

`d/dx sec(x)=sec(x)tan(x)`

You could memorize this, but you can work it out too by knowing some trig properties.

The trig properties we will use are:
`sec (x)= 1/cos(x)`
and `sin x/cos x=tan x`

Deriving:
`d/dx sec (x) = d/dx 1/cos(x) = (cos (x)(0) - 1 (-sin (x)))/( cos (x)cos (x))` (using the quotient rule)
`= sin (x)/ (cos (x) cos (x)) = sin(x)/cos(x) *(1/cos( x)) = tan (x) sec( x)=sec (x) tan (x)`