Question 380774
Use the chain rule:

{{{(d/dx) ((x^2 - 1)/(2x^3 + 1))^4 = 4 ((x^2 - 1)/(2x^3 + 1))^3 (d/dx) ((x^2 - 1)/(2x^3 + 1))}}}

By the quotient rule,

{{{(d/dx) ((x^2 - 1)/(2x^3 + 1)) = ((2x)(2x^3 + 1) - (x^2 - 1)(6x^2))/((2x^3 + 1)^2)}}}

Therefore, the derivative of {{{((x^2 - 1)/(2x^3 + 1))^4}}} with respect to x is

{{{4 ((x^2 - 1)/(2x^3 + 1))^3 ((2x)(2x^3 + 1) - (x^2 - 1)(6x^2))/((2x^3 + 1)^2)}}}

which you can simplify from there.