Question #923ff

1 Answer
Timber Lin
Dec 19, 2017

#(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)

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