Limits and Derivatives

Question

Find the derivatives of the following functions :

(x + sec x)(x - tan x)

Answer

Let y = (x + sec x)(x - tan x)
Differentiating bioth sides w.r.t. x, we get

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space dy over dx equals space space left parenthesis straight x space plus space sec space straight x right parenthesis space straight d over dx left parenthesis straight x space minus space tan space straight x right parenthesis plus left parenthesis straight x space minus space tan space straight x right parenthesis straight d over dx left parenthesis straight x plus sec space straight x right parenthesis$
$space space space space space space space space space space space space space space space space space space space equals space left parenthesis straight x plus sec right parenthesis space left parenthesis 1 plus space sec squared space straight x right parenthesis plus left parenthesis straight x minus tan space straight x right parenthesis space left parenthesis 1 plus sec space straight x space tan space straight x right parenthesis$