192. Find the derivative of the function $y=x^{2}$.

翻译完成，保留了原文的格式和换行。
Solution. Let's represent the given function as a product: $x^{2}=x \cdot x$. Now, using rule IV, we find

$$
\left(x^{2}\right)^{\prime}=(x \cdot x)^{\prime}=x^{\prime} x+x x^{\prime}=2 x
$$

since $(x)^{\prime}=1$. Therefore, $\left(x^{2}\right)^{\prime}=2 x$.