How do you find f'(x) using the definition of a derivative #f(x)= 1/x#?
1 Answer
Nov 1, 2015
Use limit definition of derivative to find:
#f'(x) = -1/x^2#
Explanation:
#f'(x) = lim_(h->0) ((f(x+h)-f(x))/h)#
#= lim_(h->0) ((1/(x+h) - 1/x)/h)#
#= lim_(h->0) ((x-(x+h))/(hx(x+h)))#
#= lim_(h->0) ((-h)/(hx(x+h)))#
#= lim_(h->0) (-1/(x(x+h)))#
#=-1/x^2#
