Question 1149041
The problem is asking the first derivative of f(x) using the limit definition of the first derivation, that is,
:
f'(x) = limit as h approaches 0 of (f(x+h) -f(x))/h
:
We are given f(x) = 1/x
:
f(x+h) = 1/(x+h)
:
f'(x) = limit as h approaches 0 of ( 1/(x+h) - 1/x) )/h =
:
(x - (x+h) ) / ( h * x * (x+h)) =
:
-h/(h * x * (x+h)) =
:
-1/(x^2 +xh)
:
h approaches 0, so we are left with
:
f'(x) = -1/x^2
: