Find the derivative of the function `sec x. tan x` with respect to `x`.

Options

A. `cos x (Secx +tanx)`
B. `cos x (Secx +tan^(2)x)`
C. `cos x (Sec^(2)x +tan^(2)x)`
D. `sec x (Sec^(2)x +tan^(2)x)`

Answer

D

Explanation

Let `Y=sec x tan x`
`rArr (dy)/(dx)=(d)/(dx)(sec x tan x)`
`=sec x. (d)/(dx)tanx+tan x.(d)/(dx)sec x`
=`secx.sec^(2)x+tanx.sec x tan x`
`=sec x (Sec^(2)x +tan^(2)x)`.