find the derivative of the transcendal function. y=`sec x/x`

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tiburtius eNotes educator| Certified Educator

Derivation of quotient:

`(f/g)'=(f' cdot g-f cdot g')/(g^2)`                                              (1)

`(sec x)'=(1/cos x)'=sin x/(cos^2 x)=secx tanx`                (2)       

Also as you probably know `x'=1`.  

Now by using rule for derivation of quotient (1) and knowing how to derivate `sec x` (2) we get

`(sec x/x)'=(sec x tan x cdot x-sec x)/(x^2)`  <-- Solution