I assume you're referring to a function,
[tex]f(x) = \dfrac{x^2}{a^2}[/tex]
where a is some unknown constant. By definition of the derivative,
[tex]\displaystyle f'(x) = \lim_{h\to0}{f(x+h)-f(x)}h[/tex]
Then
[tex]\displaystyle f'(x) = \lim_{h\to0}{\frac{(x+h)^2}{a^2}-\frac{x^2}{a^2}}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{(x+h)^2-x^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{(x^2+2xh+h^2)-x^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{2xh+h^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}(2x+h) = \boxed{\frac{2x}{a^2}}[/tex]
