How do you find the f '(x) using the definition of derivative in: #f(x)=1/x#? Calculus Derivatives Limit Definition of Derivative 1 Answer GiĆ³ Apr 20, 2015 Try this: #lim_(h->0)(1/(x+h)-1/x)/h=lim_(h->0)1/h((x-x-h)/((x+h)x))=lim_(h->0)1/h((-h)/((x+h)x))=# Simplifying #h# and taking the limit: #-1/x^2# Answer link Related questions What is the limit definition of the derivative of the function #y=f(x)# ? Ho do I use the limit definition of derivative to find #f'(x)# for #f(x)=3x^2+x# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(x+3)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/(1-x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=x^3-2# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/sqrt(x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=5x-9x^2# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(2+6x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=mx+b# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=c# ? See all questions in Limit Definition of Derivative Impact of this question 1964 views around the world You can reuse this answer Creative Commons License