The first one:
Remember that we can write the cube root as a fracitonal power, so look at it like this:
d/dx (1+(cscx)/x)^(1/3) =
(1/3)(1+(csc[x]/x))^(-2/3) * ((-xcscxcotx - cscx)/x^2)
I think this is right..
The chain rule says you bring the exponent in front, repeat the function, and take it down a power. Then you multiply that by the derivative of the inside, the derivative of the inside you would need to use the quotient rule on (low*derivative of high - high*derivative of low, all over low squared)
Hope this helps, I think it's accurate.