Hello

now, by noting that 2(h+2) is the common denominator,

now take the limit h -> 0 and you'll have the answer

There is no differencethere is another problem that says to use the alternate definition of a derivative where the numerator has f(x) - f(a), instead of (x+h). and to find the derivative at the point:

2. (with the same problem above.)

What Is The Difference and what accounts for that difference?

from the first one to the second one, you just have to substitute