Derivative from Definition (square roots)

[I_LuV_FiZiX]

Homework Statement

Find the derivative from definition of the functin f(x)= x + squareroot(x)

Homework Equations

The Attempt at a Solution

I only got as far as where I canceled out my positive and negative x terms in the numerator, and am left with three terms (2 of which are square roots, the other being an h), and I am wondering what to do now; is there some way to multiply by the conjugate?

 

[statdad]

The difference quotient should look like

$$\frac{((x+h) + \sqrt{x+h}) - (x + \sqrt x)}{(x+h)-x} = \frac{h + (\sqrt{x+h} - \sqrt x)}{h},$$

does it not? try splitting it into 2 fractions (based on the grouping I've shown above). One of the fractions is quite simple, the other you can simplify with the method you mentioned in your post. After the fractions are simplified, bring in the limits as $$h \to 0$$