1) if you have 4x^(-2), and you wanted to make the power positive, would you bring the coefficient to the bottom?

e.g. 1/(4x^2) -OR- 4/(x^2)

2) find the derivative of (sqrt(x)-1)/(sqrt(x)+1)

I understand the quotient rule and syntax, it just doesn't work out to the answer that I've been given... PROBABLY a simplification error... here's what I did:

{(x½+1)(1/2x-½)-(x½-1)(1/2x-½)}/(x½+1)^2

(1/2)+(1/2x-½)-(1/2)+(1/2x-½)

x-½/(x½+1)^2

what I get:

1/(x^2(x½+1)^2)

and the answer is 1/(x½(x½+1)^2)

3) why is it that when you look at the cuberoot function (x^(1/3)) from left to right, you see its slope is always positive (albeit undefined at x=0), yet the derivative (1/3x^(-1/3)) shows that its slope is negative from a domain of negative infinity to 0? should it not be positive?

thanks.