What is the derivative of #tan^-1 (3x^2 +1)#?
1 Answer
Apr 11, 2016
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) #
