Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 45

We know that $(uvw)'=u'vw+uv'w+uvw'$ $\implies \frac{d}{dx}(x^{3})=\frac{d}{dx}(x\cdot x\cdot x)$ $=\frac{d}{dx}(x)\cdot x\cdot x+x\cdot \frac{d}{dx}(x)\cdot x+x\cdot x\cdot \frac{d}{dx}(x)$ $=x^{2}+x^{2}+x^{2}=3x^{2}$

See the answer above.