Question

Quick differentiation problem:
Differentiate x(1-x^2)^1/2

Answer 1

So what's your best guess?

Answer 2

I'm doing power rule and a chain rule in there, but I'm not getting the right answer

Answer 3

Also product rule
http://www.wolframalpha.com/input/?i=derivative++x%281-x^2%29^%281%2F2%29

Answer 4

what answer do you get?

Answer 5

Yeah, remember you have x times sqrt(1-x^2). So you can either do the product rule or change it to:

sqrt(x^2-x^4).

Check that the answers you get from doing product rule or by bringing it inside the square root both give the same answer. Be amazed at the magical consistency calculus.