Step-by-step explanation:
[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{f(x + h) - f(x)}{h}[/tex]
[tex]\:\:\:\:\:\displaystyle = \lim_{h \to 0} \dfrac{(x+h)^2 -7 -(x^2 - 7)}{h}[/tex]
[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} \dfrac{(x^2 +2hx + h^2 -7) - (x^2 -7)}{h}[/tex]
[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} \dfrac{2hx + h^2}{h}[/tex]
[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} (2x +h)[/tex]
[tex]\:\:\:\:\: \displaystyle= 2x[/tex]
