If $y = x^{2} \log x$, what is $\frac{d^2y}{dx^2}$?

Explanation

1. 01

   First derivative: $\frac{dy}{dx} = x \left(2 \log x + 1\right)$.

2. 02

   Differentiate again: $\frac{d^2y}{dx^2} = 2 \log x + 3$.