How do you find f'(x) using the definition of a derivative for #f(x)= 6 x + 2sqrt{x}#? Calculus Derivatives Limit Definition of Derivative 1 Answer Konstantinos Michailidis Oct 8, 2015 The derivative is #f'(x)=lim_(h->0)(f(x+h)-f(x))/h=lim_(h->0)(6(x+h)+2sqrt(x+h)-6x-2sqrtx)/h=lim_(h->0) 6+2*(sqrt(x+h)-sqrtx)/h= 6+2lim_(h->0)(sqrt(x+h)-sqrtx)/h= 6+2lim_(h->0)h/(h(sqrt(x+h)+sqrtx))=6+2*1/(2sqrtx)=6+1/sqrtx# 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 1405 views around the world You can reuse this answer Creative Commons License