How do you find the derivative of #f(x) = 7x^2 - 3 # using the limit definition? Calculus Derivatives Limit Definition of Derivative 1 Answer Eddie Jun 22, 2016 #14x# Explanation: f#'(x) = lim_{h \to 0} ( (7(x+h)^2 - 3) - (7x^2 - 3))/h# # = lim_{h \to 0} ( (7(x^2+2xh + h^2) - 3) - (7x^2 - 3))/h# # = lim_{h \to 0} ( 7x^2+14xh + 7h^2 - 3 - 7x^2 + 3)/h# # = lim_{h \to 0} ( 14xh + 7h^2 )/h# # = lim_{h \to 0} 14x + 7h = 14x# 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 5018 views around the world You can reuse this answer Creative Commons License