If #f(x)=4x^(-1)# find #(f(a+h)-f(a))/h#? Calculus Derivatives Limit Definition of Derivative 1 Answer Shwetank Mauria Feb 25, 2017 #(f(a+h)-f(a))/h=(-4)/(a(a+h))# Explanation: As #f(x)=4x^(-1)=4/x# as such #f(a)=4/a# and #f(a+h)=4/(a+h)# and #(f(a+h)-f(a))/h=(4/(a+h)-4/a)/h# = #((4a-4a-4h)/(a(a+h)))/h# = #((-4h)/(a(a+h)))/h# = #(-4h)/(a(a+h))xx1/h# = #(-4)/(a(a+h))# 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 2127 views around the world You can reuse this answer Creative Commons License