What is the derivative of #arctan(x^2+1)#?

1 Answer
Mar 17, 2016

#(2x)/(x^4 + 2x^2 + 2 ) #

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) #