How do you differentiate sin rootx?

By the chain rule, the derivative of sin(x1/2) will be the derivative of x1/2 multiplied by the derivative of the enclosing sine function. Thus,

y = sin(x1/2)

y' = (1/2)*(x-1/2)*cos(x1/2)

For further reading, you might want to consult your calculus book on the chain rule. Here is a site that (kind of) explains the chain rule, though it does have good examples: http://archives.math.utk.edu/visual.calculus/2/chain_rule.4/index.html

For step-by-step derivatives of functions, try Calc 101: http://calc101.com/webMathematica/derivatives.jsp