How to differentiate 3/x^2 + 5x^2

My interpretation: \({d\over dx}({3\over x^2}+5x^2)\)

By sum rule: \({d\over dx}{3\over x^2}+{d\over dx}5x^2\)

By definition of negative exponents: \({d\over dx}3x^{-2}+{d\over dx}5x^2\)

By constant product rule: \(3({d\over dx}x^{-2})+5({d\over dx}x^2)\)

By power rule: \(3(-2x^{-3})+5(2x)\)

Simplify to get \(10x-{6\over x^3}\), which is your final answer.