How do you find f'(x) using the definition of a derivative for f(x)= 6 x + 2sqrt{x}f(x)=6x+2√x?

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

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