Hi guys and girls, long time no see. I've been away for the Christmas holidays (away from my computer at least) but now I am back to bug you with more laughably simple questions!

I've moved on to the topic of calculus and am having a little trouble with some differentiation questions. I understand how to do basic questions such as y=x^10 dy/dx = 10x^9.

I think these are also correct, only my book shows the answers in a different format, I'd be obliged if you could check.

y = 1/x = x^-1 dy/dx = -x^-2 (book says: -1/x^2)

y=sqrt x = x^1/2 dy/dx = 1/2x^-1/2 (book says: 1/ 2sqrt x)

y= -1/x^4 = -x^-4 dy/dx = 4x^-3 (book says: 4/x^5)

P.S. Happy New Year!