Using the limit definition, let f(x) = x3. Find f'(1).
Yes, we do need to cube (1 + h).
We have a = 1 and f(x) = x3. We plug this into the limit definition of the derivative:
Since (1 + h)3 is not quite a barrel of monkeys, we need to work it out separately here and then put it back in the formula. This requires the Distributive Law and combining like terms.
Now back we go:
Therefore f'(1) = 3.