I'm not sure about the result.

f(x)= (x^{3}+x^{2})/(x^{2}-4)

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

=(3x^{4}+2x^{3}-12x^{2}-8x) - (2x^{4}+ 2x^{3}) / (x^{2}-4)^{2 }

=(x^{4}-12x^{2}-8x) / (x^{2}-4)^{2 Would this be the simplified first derivative?}