How do you find f'(x) using the definition of a derivative for f(x)=(4/x^2) ? Calculus Derivatives Limit Definition of Derivative 1 Answer Sasha P. Oct 20, 2015 See the explanation. Explanation: f'(x)=lim_(h->0) (f(x+h)-f(x))/h f'(x)=lim_(h->0) (4/(x+h)^2-4/x^2)/h = lim_(h->0) ((4x^2-4(x+h)^2)/(x^2(x+h)^2))/h f'(x)= lim_(h->0) (4x^2-4x^2-8xh-4h^2)/(hx^2(x+h)^2) f'(x)= lim_(h->0) (-8xh-4h^2)/(hx^2(x+h)^2) = lim_(h->0) (-8x-4h)/(x^2(x+h)^2) = (-8x)/(x^2x^2) f'(x)= -8/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 1718 views around the world You can reuse this answer Creative Commons License