Differentiate the following functions with respect to x :
`(x^(2) + 4/(x^(2)) - 2/3 tan x + 6e)`

Options

A. `x - 8/(x^(3)) - 1/3 sec^(2)x`
B. `2x - 2/(x^(3)) - 1/3 sec^(2)x`
C. `2x - 8/(x^(3)) - 1/3 sec^(2)x`
D. `2x - 8/(x^(3)) - 2/3 sec^(2)x`

Answer

D

Explanation

`d/(dx) (x^(2) + 4/(x^(2)) - 2/3 tan x + 6e)`
`= d/(dx) (x^(2)) 4.d/(dx) (x^(-2)) - 2/3.d/(dx) (tan x) + 6.(d)/(dx) (e )`
`= 2x + 4 .(-2) x^(-3) - 2/3 sec^(2) x + 6 xx 0" "[:' d/(dx) (e ) = 0]`
`=2x - 8/(x^(3)) - 2/3 sec^(2)x`.