Compute f'(a) in Two Ways

Question

f(x)=x²+9x, a=0

Answer 1

First way: f'(0) = lim_x→0[(f(x) - f(0)) / (x-0)]

= lim_x→0[(x² + 9x) / x] = lim_x→0[(x(x+9)/x] = lim_x→0[x+9] = 9

Second method:

f'(x) = 2x + 9

So, f'(0) = 2(0) + 9 = 9