ok. So if the ^5 is the house and the (x+1) is the man inside the house, you have to take the derivative of the house before the man. This is the chain rule.
using this logic, we get this answer:
5(x+1)^4 * 1
house man

to take the double derivative we use the same process, giving us 20(x+1)^3 *1

the same logic goes for the second one, but instead the chain rule gives us not just a "*1" as it did in the last one. the man inside the house is (x^2-x+1) and the derivative of that is (2x-1) so you have to multiply that one by the exponent derivative, aka the house.
3(x^2-x+1)^2 *(2x-1)
the second derivative of this uses the product rule. f'g+g'f, as well as the chain rule.

You can also do all of this easily on a calculator. especially a TI-89

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