First Principles Calculus (Essay Sample)

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First Principles: Calculus
Finding the first derivative of Y = x2 using the first principle:
y = x2
In function form,
F (x) = x 2
The above expression can be expanded into the following
F (x + h) = (x + h) 2
From the first principle,
Lim f (x + h) – f (x)
h → 0h
Therefore; Lim (x + h) 2 – (x) 2
h → 0h
x 2 + 2x + h 2 – x 2
h
The expression above results into the following,
h (2x + h)
h
The h...