If the slope of the secant line is 19/(sqrt(19x-2)+sqrt(19(x+h)-2) and as h approaches 0, what would the slope of the tangent line to the graph of f at point (x,f(x)) be?
Keep going. As h continue to get decrease in magnitude, you should get an even simpler expression. When you get this expression, call it f'(x), you can evaluate the expression at the same point and you will get the slope fo the tangent line. If your point is (a,f(a)), your tangent line should be y-f(a) = f'(a) * (x-a). Isn't this in your book?