Question

Find the derivative of f(x) = 9x + 5 at x = 7.

Answer 1

$f(x)=9x+5\implies f'(x)=9\implies f'(7)=9$

Or, using the definition of the derivative,

$f'(7)=\displaystyle\lim_{x\to7}\frac{f(x)-f(7)}{x-7}$

$\displaystyle=\lim_{x\to7}\frac{(9x+5)-(63+5)}{x-7}$

$\displaystyle=\lim_{x\to7}\frac{9(x-7)}{x-7}$

$\displaystyle=\lim_{x\to7}9=9$