School and Work

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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does it simply mean that the distance between objects in the universe is expanding, while the size of the objects remains the same, or would the objects in the universe increase in size at the same rate at which the distance between such objects expands?

and also if the former is true, at some point wouldn't the distance between for example, the earth and our sun, increase to such a distance at which the earth would no longer be inhabitable due to the decrease in temperature?

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