How do you find the derivative of the function #f(x)=x^2-3x# using #f(x+h)-f(x)/h#? Calculus Derivatives Limit Definition of Derivative 1 Answer Tiago Hands · Massimiliano Apr 20, 2015 Know that: #f'(x)=lim_(hrarr0)(f(x+h)-f(x))/h# #=lim_(hrarr0)((x+h)^2-3(x+h)-(x^2-3x))/h# #=lim_(hrarr0)(x^2+2xh+h^2-3x-3h-x^2+3x)/(h)# #=lim_(hrarr0)(h^2+2xh-3h)/(h)# #=lim_(hrarr0)(h(h+2x-3))/(h)# #=lim_(hrarr0)h+2x-3# #=2x-3# 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 5312 views around the world You can reuse this answer Creative Commons License