If (below), then f'(x) = ? (A) 3 (B) 1 (C) -1 (D) -3 (E) -5 #f(x)=(-x^4+x^2+1)/x# Calculus Derivatives Limit Definition of Derivative 1 Answer Jim H Nov 1, 2016 None of these. #f'(x) = -3x^2+1-1/x^2# Explanation: #f(x) = (-x^4+x^2+1)/x = -x^3+x+1/x# #f'(x) = -3x^2+1-1/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 1590 views around the world You can reuse this answer Creative Commons License