If function $f$ is differentiable at a point $a$, does it imply that $f'(a)$ exists?
I want to proof that if function $f$ is differentiable at a point $a$, then the function is continious at this point. I want to do this by using the multiplication rule for limits. For that I need to show that function $f$ has a finite limit at point $a$. I have read that function if is differentiable at a point $a$ if $f'(a)$ exists. However, it seems that it is not exactly what I need.
Thank you for your asnwers. I was a bit confused by how the definiton phrased.
I have an additional question: how does one know when "if" means "if and only if" and "if" means "if"?