194. Find the derivative of the function $y=x^{3}$.

翻译完成，保留了原文的格式和换行。
Solution. Representing the given function as a product: $x^{3}=x^{2} \cdot x$ and applying rule IV again, we find

$$
\left(x^{3}\right)^{\prime}=\left(x^{2} \cdot x\right)^{\prime}=\left(x^{2}\right)^{\prime} \cdot x+(x)^{\prime} \cdot x^{2}=2 x \cdot x+1 \cdot x^{2}=2 x^{2}+x^{2}=3 x^{2}
$$