SOLUTION: Differentiate Sqrt{1-x^2}

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Question 884172: Differentiate Sqrt{1-x^2}
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1) sqrt%281-x%5E2%29 or
(2) %281-x%5E2%29%5E%281%2F2%29
Let
(3) u = (1-x^2) and rewrite (2) as
(4) u^(1/2)
Now take the derivitive of (3) and get
(5) ((1/2)u^(1/2-1))*du/dx or
(6) ((1/2)*(1/u^(1/2)))*du/dx
Now get du/dx from (3)
(7) du/dx = d((1-x^2)/dx or
(8) du/dx = -2x
Now put (8) into (6) to get
(9) ((1/2)*(1/u^(1/2)))*(-2x) or
(10) -x%2Fsqrt%281-x%5E2%29