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 1649 views around the world You can reuse this answer Creative Commons License