Using the definition of derivative. f′(4)

Question

If f(x) = sqrt(3+4x), find f′(4), using the definition of derivative. f′(4)  is the limit as x→_____ of the expression ____. The value of the limit is ____

I know the first blank is 4 and the third blank is .45883146. I don't understand how t find the expression. thank you for any help you may provide.  

Answer 1

f'(4) = lim x→4 (f(x) - f(4)/(x - 4) = lim x→4 (√3 + 4x - √19)/(x - 4) = lim x→4 (3 + 4x - 19)/[(x - 4)(√3 + 4x √19)] =

= 4/(√19 + √19) = 2/√19