How do you find f'(x) using the definition of a derivative for f(x)=sqrt(2x-1)f(x)=√2x−1? Calculus Derivatives Limit Definition of Derivative 1 Answer Sasha P. Oct 5, 2015 See the explanation. Explanation: f'(x)=lim_(h->0) (f(x+h)-f(x))/h f'(x)=lim_(h->0) (sqrt(2(x+h)-1)-sqrt(2x-1))/h= =lim_(h->0) (sqrt(2(x+h)-1)-sqrt(2x-1))/h * (sqrt(2(x+h)+1)+sqrt(2x-1))/(sqrt(2(x+h)-1)+sqrt(2x-1)) =lim_(h->0) ((2(x+h)-1)-(2x-1))/(h(sqrt(2(x+h)-1)+sqrt(2x-1))) =lim_(h->0) (2x+2h-1-2x+1)/(h(sqrt(2(x+h)-1)+sqrt(2x-1))) =lim_(h->0) (2h)/(h(sqrt(2(x+h)-1)+sqrt(2x-1))) =lim_(h->0) 2/(sqrt(2(x+h)-1)+sqrt(2x-1)) =lim_(h->0) 2/(2sqrt(2x-1))=1/sqrt(2x-1) 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 4264 views around the world You can reuse this answer Creative Commons License