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This is Ana's definition of the derivative:

Find f '(x) and then the limit will equal f '(0).

Or you could multiply the numerator and denominator by the conjugate of the numerator.

Evaluate. The denominator will not equal zero so the limit and the actual value agree at x = 2.

Rewrite the absolute value as a piecewise function but, since x → 2+, only consider the piece in which x > 2.

Think about what the graph of y = ex looks like. What does it look like all the way to the right, as x → ∞? How does the +1 affect the graph?