Hi, I'm starting derivatives and I am getting confused. Some problems seem easier solved by

f(x)-f(a)

---------

x - a

As x approaches a

and some by

f(a+h)-f(a)

-----------

h

as h approaches 0

Why is this and how do I choose the best option? Does it matter if it's a velocity problem and not a tangent problem? I thought they were the same. Does it matter if I have a point (c,f(c)) to go off of? I apologize if I'm not making much sense, but I have practiced both methods and still don't understand why they are different.