Starting with x^(1/2) * e^x
i have gotten to g`(x) = x^(1/2)(e^x) + e^x(1/2x^(-1/2))
what would be the next algebraic (sp) step?
You could also move the $\displaystyle x^{-\frac{1}{2}}$ to the denominator as $\displaystyle \sqrt x$
$\displaystyle \frac{e^x}{2\sqrt x} + e^x\sqrt x$
I guess if you wanted to do more, you could get a common denominator and combine the two. Not sure how far your teacher wants you to take it.