Question

1/X by first principles

Answer 1

What do you want, the derivative?
if so
f(x) = 1/x
f(x+h) = 1/(x+h)

f(x+h)-f(x) = 1/(x+h) - 1/x

= [ x -(x+h)] /[x(x+h)]

= -h/ (x^2 + x h)

[f(x+h)-f(x)]/h = -1/(x^2+xh)

limit as h-->0
= -1/x^2

which is of course the derivative

Answer 2

Where did -h come from

Answer 3

h is a small increase in x which is allowed to approach zero to get the slope of f(x) at x, the definition of the derivative

Definition of deriviative of f(x) is:
df/dx = {f(x+h) - f(x) ]/h as h-->0

Answer 4

Oh, if you mean the algebra look at the numerator
[ x -(x+h)] = x - x - h
= -h