Find the derivative. State the domain of the function and the domain of its derivative.
f(x) = x + √x
f(x) = (3 + x) / 1-3x
Find F'(a)
f(x) = (x^2 + 1) / (x - 2)
f(x) = √3x + 1
What's giving you trouble?
For the first, rewrite: $\displaystyle x + \sqrt x = x + x^{1/2}$ and use the power rule. The second can be done simply with the quotient rule.
The third can also be done with the quotient rule, but it would be easier to reduce the fraction (factor the numerator).
For the fourth, use the chain rule:
$\displaystyle \frac d{dx}\left[\sqrt{3x} + 1\right] = \frac d{dx}\left[(3x)^{1/2} + 1\right] = \frac12(3x)^{-1/2}\frac d{dx}\left[3x\right]$