Question

Question #923ff

Answer 1

`(tan(2x)+2x(sec(2x))^2)/(xtan(2x))`

Explanation:

`d/dx(ln(xtan(2x)))`
`=1/(xtan(2x))*d/dx(xtan(2x))` (ln(x) derivative and chain rule)

`=1/(xtan(2x))[tan(2x)*d/dx(x)+x*d/dx(tan(2x))]` (product rule)

`=1/(xtan(2x))[tan(2x)*1+x*(sec(2x))^2*d/dx(2x)]` (tanx derivative)

`=1/(xtan(2x))[tan(2x)+x(sec(2x))^2*2]`
`=(tan(2x)+2x(sec(2x))^2)/(xtan(2x))`

(you can do further simplification if you want)