What is the second derivative of f(x) = sec x

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find the second derivative of f(x) = sec x

f'(x) = sec x* tan x

use the product rule

f''(x) = (sec x * tan x)'

=> (sec x)'*tan x + sec x*(tan x)'

=> sec x * tan x*tan x + sec x * (sec x)^2

=> sec x * (tan x)^2 + (sec x)^3

=> sec x[(tan x)^2 + (sec x)^2]

=> sec x[ (tan x)^2 + 1 + (tan x)^2]

=> sec x*(1 + 2*(tan x)^2)

The second derivative of f(x) = sec x is sec x*(1 + 2*(tan x)^2)

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