Question

using the definition
f '(a)= lim (f(a+h)-f(a))/h
h->0

determine the derivative of f(x)=1/x at the point x=2

Answer 1

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

1 1
----- - ----
h(x+h) hx


x x+h
----- - -------
hx(x+h) hx(x+h)



x-x+h
----------
hx(x+h)


1
-------
x(x+h)

Answer 2

dropped a (-)

Answer 3

x (x+h)
----- - -------
hx(x+h) hx(x+h)



x-(x+h)
----------
hx(x+h)

x-x-h
----------
hx(x+h)



-h
-------
hx(x+h)

-1 -1 -1
-------; -------- = -----
x(x+h) x(x+0) x^2

Answer 4

lol, amistre to the rescue again. ok, so the derivative is -1/x^2. What does the point x=2 change when deriving this?

Answer 5

-1/2^2=-1/4