differentiate the cube root of (1+3xsquare)square.everytin over x

Answer 1

f(x) = (1+3x^2)^(1/3) / x

f'(x) =
((1/3)(1+3x^2)^(-2/3) * 6x)(x) - (1+3x^2)^(1/3)(1)
----------------------------------------------------
x^2

-(x^2+1)
-------------------------
x^2 (1+3x^2)^(2/3)