Using a limit and the difference quotient, write the definition of the derivative at point a

a )f'(a)=

b) Use the definition to compute f'(2) if f(x)=2x^2+9

I have
A) lim(h->) [f(x+h)-f(x)]/h
f'(a)= f(a+h)-f(a)/h

B) f(x+h)= 2(x+h)^2+9
= (2x^2+4xh+2h^2+9)-(2x^2+9)/h
= 4xh+2h^2/h
= 4x+2h

lim =4(2)+2h
x->2

= 8+2h or = 8 ?

a)
lim(h->) [f(x+h)-f(x)]/h ........... h -> what? Should be: f'(x) = lim (h -> 0) [f(x+h)-f(x)]/h
f'(a)= f(a+h)-f(a)/h ............ Where's the limit? Should be f'(a)= lim (h -> 0) [f(a+h)-f(a)]/h

b)
f(x+h)= 2(x+h)^2+9 ..........True, but don't forget the limit
= (2x^2+4xh+2h^2+9)-(2x^2+9)/h .......... OK, but still no limit
= 4xh+2h^2/h .......... Should be f'(x) = lim (h -> 0) 4xh+2h^2/h
= 4x+2h ............. Should be f'(x) = lim (h -> 0) 4x+2h
f'(x) = 4x

f'(2) = 8