Posted by Tom Lahay on November 11, 2002 at 14:53:47:
I have a problem when simplifying one of my answers.
y'=(1-x^3) * x - 3x^2 * SQRT(1+x^2)
Simplifying, my book states the first step as:
y' = ---------- [1 - x^3 - 3x(1+x^2)]
I see that the result is one less power of 3x and the next expression is no longer square rooted but I am unsure why. I am missing some small algebra trick that I have forgotten over time and my only hypothesis is:
Because SQRT(1+x^2) = (1+x^2)^1/2
If I mutiply the power of -3x^2 by the power of the expression (1+x^2)^1/2 then it may follow that:
-3x(1+x^2) since 2*1/2=1
Is it because 1/2 is a common factor or what? Any proofs, explanations would be appreciated.
Then next step makes complete sense to me but I would like the full picture.
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