Find the derivative of f(x)=x^2-3 by the limit process

Answer 1

f(x) = x^2 -3

f(x+h) = (x+h)^2 -3 = x^2+2xh+h^2 -3

f(x+h)-f(x) = 2xh+h^2

[f(x+h)-f(x)]/h = 2x+h

limit as h approaches 0 is 2x+0 = 2x = f'(x)