Qual é a derivada do #arctan (2x) #?
Responda:
# 2/(1+4x^2)#
Explicação:
using # d/dx (tan^-1x) = 1/(1+x^2)#
differentiating using the #color(blue)(" chain rule ")#
here x = 2x , hence
#rArr d/dx(tan^-1 2x) = 1/(1+(2x)^2) d/dx(2x) #
# = 1/(1+4x^2) .2 = 2/(1+4x^2) #