In order to prove a certain function in $\mathbb{R}^2$ is totally differentiable, I have to make the following step: $xy ≤ 0.5(x^2+y^2)$. However, I do not understand why this inequality holds. I do understand both $x$ and $y$ are smaller than the norm $\|x\|$, which would create the inequality $xy ≤ x^2+y^2$, but that expression is not small enough to justify the inequality.