What is the derivative of #tan^-1 (3x^2 +1)#?

1 Answer
Apr 11, 2016

#(6x)/(9x^4 + 6x^2 + 2)#

Explanation:

differentiate using the #color(blue)" chain rule " #

#d/dx [ f(g(x)) ] = f'(g(x)) . g'(x) #

and the standard derivative : D#(tan^-1 x) = 1/(1 + x^2)#
#"--------------------------------------------------------------------------"#

f(g(x)) #= tan^-1(3x^2 + 1) rArr f'(g(x)) = 1/(1 + (3x^2 + 1)^2)#

and g(x) # = 3x^2 + 1 rArr g'(x) = 6x #
#"----------------------------------------------------------------------"#

#rArr f'(g(x)). g'(x) = 1/(1 +9x^4+ 6x^2 + 1 ) .6x#

# = (6x)/(9x^4 +6x^2 + 2) #