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 ยท 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 5724 views around the world You can reuse this answer Creative Commons License