`y = sec(x)/x` Find the derivative of the trigonometric function.

Textbook Question

Chapter 2, 2.3 - Problem 48 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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Note:- 1) If y = secx ; then dy/dx = secx*tanx

2) If y = x^n ; then dy/dx = n*x^(n-1) ; where n = constant

3) If y = u/v ; where 'u' & 'v' are functions of 'x' , then dy/dx = [vu'-uv']/(v^2)

Now, 

`y = sec(x)/x`

`dy/dx = y' = [x*sec(x)*tan(x) - sec(x)]/x^2`

`or, y' = dy/dx = sec(x)*[xtan(x)-1]/(x^2)`

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