Find the derivative of the following functions by definition:
1. f (x) = 2x + 3. Find f'(1) and f′(a), a ∈ R.

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Answers:

f ' (1) = 2

f ' (a) = 2

Work Shown

f(x) = 2x + 3

f ' (x) = 2

f ' (1) = 2

f ' (a) = 2

It turns out that no matter what input you plug in, the derivative output is always 2. This is the slope of the line. The plus 3 at the end does not affect the derivative since that portion goes to zero.