How do you use the definition of a derivative to find the derivative of #f(x)=x^2 - 1#, at c=2? Calculus Derivatives Limit Definition of Derivative 1 Answer salamat Jan 23, 2017 #4# Explanation: let #x_1=2# #f'(x)=lim_(x->x_1)(f(x)-f(x_1))/(x-x_1)# #=lim_(x->2)((x^2-1)-(2^2-1))/(x-2)# #=lim_(x->2)(x^2-1-3)/(x-2)# #=lim_(x->2)(x^2-4)/(x-2)# #=lim_(x->2)((x+2)(cancel(x-2)))/cancel(x-2)# #=lim_(x->2)(x+2)# #=2+2=4# 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 1199 views around the world You can reuse this answer Creative Commons License