[tex]f(x)=9x+5\implies f'(x)=9\implies f'(7)=9[/tex]
Or, using the definition of the derivative,
[tex]f'(7)=\displaystyle\lim_{x\to7}\frac{f(x)-f(7)}{x-7}[/tex]
[tex]\displaystyle=\lim_{x\to7}\frac{(9x+5)-(63+5)}{x-7}[/tex]
[tex]\displaystyle=\lim_{x\to7}\frac{9(x-7)}{x-7}[/tex]
[tex]\displaystyle=\lim_{x\to7}9=9[/tex]
