How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(x+3)# ? Calculus Derivatives Limit Definition of Derivative 1 Answer Andrea S. May 25, 2018 #d/dx (sqrt(x+3)) = 1/ (2sqrt(x+3)# Explanation: By definition: #d/dx (sqrt(x+3)) = lim_(h->0) (sqrt(x+h+3)-sqrt(x+3))/h# #d/dx (sqrt(x+3)) = lim_(h->0) ((sqrt(x+h+3)-sqrt(x+3))/h)( (sqrt(x+h+3)+sqrt(x+3))/ (sqrt(x+h+3)+sqrt(x+3)))# #d/dx (sqrt(x+3)) = lim_(h->0) ((x+h+3)-(x+3))/(h (sqrt(x+h+3)+sqrt(x+3))# #d/dx (sqrt(x+3)) = lim_(h->0) h/(h (sqrt(x+h+3)+sqrt(x+3))# #d/dx (sqrt(x+3)) = lim_(h->0) 1/ (sqrt(x+h+3)+sqrt(x+3)# #d/dx (sqrt(x+3)) = 1/ (2sqrt(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)=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# ? How do I us the Limit definition of derivative on #f(x)= 1/x#? See all questions in Limit Definition of Derivative Impact of this question 13026 views around the world You can reuse this answer Creative Commons License