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

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jesuhlocun103 | Student, College Freshman | (Level 1) Honors

Posted February 20, 2013 at 6:44 PM via web

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find the derivative of the transcendal function.

y=`sec x/x`

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted February 20, 2013 at 7:22 PM (Answer #1)

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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

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