How do you use the limit definition to find the derivative of #y=-3x-3#? Calculus Derivatives Limit Definition of Derivative 1 Answer Steve M Oct 15, 2016 # dy/dx=-3# Explanation: By definition: # dy/dx=lim_(h->0)(f(x+h)-f(x))/h # so, with # y=-3x-3 # we have: # dy/dx=lim_(h->0)((((-3)(x+h)-3)-(-3x-3))/h)# # :. dy/dx=lim_(h->0)((-3x -3h-3+3x+3)/h)# # :. dy/dx=lim_(h->0)(-3h)/h# # :. dy/dx=-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 1611 views around the world You can reuse this answer Creative Commons License