TeX source:

\begin{aligned}\frac{d y}{\mathrm{dx}}=& \lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}=\lim\limits_{h \rightarrow 0} \frac{\left\{x^{3}+3 x^{2} h+3 x h^{2}+h^{3}\right\}-x^{n}}{h} \\&=\lim _{h \rightarrow 0} \frac{3 x^{2} h+3 x h^{2}+h^{3}}{h}=\lim\limits_{h \rightarrow 0}\left(3 x^{2}+3 x h+h^{2}\right)=3 \mathbf{x}^{2}\end{aligned}