Question

derivative of f(x)= xtanx

Answer 1

use the product rule
if y = uv then y ' = vu' + uv'

Answer 2

let u = x ---> u' = 1
v = tan(x) ---> v' = sec^2 (x)

now, aplly them to formula above

Answer 3

so it would be tan(x)+ sec^2(x) (x)?

Answer 4

yes
or it can be modificated again
use the identity :
sec^2 (x) = tan^2 (x) + 1

tan(x)+ sec^2(x) (x)
= tan(x)+ (tan^2(x) + 1) (x)
= xtan^2 (x) + tan(x) + x