What is the derivative of this function #arctan(e^x)#?
1 Answer
Jun 17, 2017
Explanation:
#"differentiate using the "color(blue)"chain rule"#
#color(orange)"Reminders"#
#• d/dx(tan^-1x)=1/(1+x^2)#
#• d/dx(tan^-1(f(x)))=1/(1+f(x)^2)xxf'(x)larr" chain rule"#
#rArrd/dx(tan^-1(e^x))#
#=1/(1+(e^x)^2)xxd/dx(e^x)#
#=e^x/(1+e^(2x))#
