How do you find the derivative of #f(x)=-5x# using the limit process? Calculus Derivatives Limit Definition of Derivative 1 Answer sjc Nov 3, 2017 see below Explanation: the definition #(dy)/(dx)=Lim_(hrarr0)((f(x+h)-f(x))/h)# #f(x)=-5x# #(dy)/(dx)=Lim_(hrarr0)((-5(x+h)- (-5x))/h)# #(dy)/(dx)=Lim_(hrarr0)((cancel(-5x)-5hcancel(+5x))/h)# #(dy)/(dx)=Lim_(hrarr0)((-5cancel(h))/cancel(h))# #(dy)/(dx)=Lim_(hrarr0)(-5)=-5# 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 3483 views around the world You can reuse this answer Creative Commons License