What is the third derivative of y = sin x + cos x + tan x

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justaguide eNotes educator| Certified Educator

The function `y = sin x + cos x + tan x` . The derivatives of the function are:

`y' = cos x - sin x + sec^2x`

`y'' = -sin x - cos x + 2*sec x*sec x*tan x`

`y'' = -cos x + sin x + 2*2*sec x*sec x*tan x*tan x`

` + 2*sec^2x*sec^2x`

= `-cos x + sin x + 4*sec^2x*tan^2x + 2*sec^4 x`

The required derivative is `y' = -cos x + sin x + 4*sec^2x*tan^2x + 2*sec^4 x`

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