Question #69fe4

1 Answer
Eddie
Apr 7, 2017

See below

Explanation:

For #f(x) = 1/x#:

#f'(x) = lim_(h to 0) (1/(x+h) - 1/x)/h#

# = lim_(h to 0) ((x - (x+h))/(x(x+h)))/h#

# = lim_(h to 0) - (h/(x(x+h)))/h#

# = lim_(h to 0) - 1/(x(x+h)) = -1/x^2#

For #f(x) = x#:

#f'(x) = lim_(h to 0) ((x+h) - x)/h#

#= lim_(h to 0) h/h = 1#

That should be enough, whatever yr question is.

Related questions
See all questions in First Principles Example 1: x²
Impact of this question
2689 views around the world
You can reuse this answer
Creative Commons License