differentiate: y=[xcos(x^3)]/[(x^4 + 1)^3] with respect to x

This question is on the trickier side as it is heavily computational and requires a good knowledge of the differentiation rules however it is a good way to practise using multiple rules at once.First we will use the quotient rule formula: dy/dx = [vdu-udv]/[v²]we will set: u = xcos(x³) and v = (x⁴+1)³by using the product and chain rule we can the calculate du = cos(x³) - 3x³sin(x³) and dv = 12x³(x⁴ + 1)²substituting these values into the quotient rule formula we get: dy/dx = { (x⁴ + 1)³[cos(x³) - 3x³sin(x³)] - 12x⁴cos(x³)(x⁴ + 1)² }/{(x⁴ + 1)⁶}Finally, after simplifying we achieve: dy/dx = { cos(x³)(1 - 11x⁴) - 3x²sin(x³)(1 + x⁵) }/{(x⁴ + 1)⁴}