What is the derivative of #arctan(x^2+1)#?
1 Answer
Mar 17, 2016
Explanation:
Using the
#color(blue)" chain rule " #
# d/dx [ f(g(x)) ] = f'(g(x)) . g'(x) # and the standard derivative
# d/dx(tan^-1 x) = 1/(1 + x^2) #
# rArr d/dx(tan^-1(x^2+1)) = 1/(1+(x^2+1)^2) . d/dx(x^2+1) #
# = (2x)/(1+x^4+2x^2+1) = (2x)/(x^4+2x^2+2) #
