How do you find f'(x) using the definition of a derivative for #f(x)=1/x^2#? Calculus Derivatives Limit Definition of Derivative 1 Answer cspark1981 Oct 15, 2015 # f'(x) = -2/x^3 # Explanation: # f(x) = 1/x^2 # # f'(x) = lim_(h \rarr 0) (f(x+h) - f(x))/h # # = lim_(h \rarr 0) (1/(x+h)^2 - 1/x^2)/h # # = lim_(h \rarr 0) (x^2 - (x+h)^2)/(h(x+h)^2x^2) # # = lim_(h \rarr 0) (-2xh-h^2)/(h(x+h)^2x^2) # # = lim_(h \rarr 0) (-2x-h)/((x+h)^2x^2) # # = -2/x^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 1490 views around the world You can reuse this answer Creative Commons License