- #1
maphco
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Homework Statement
Differentiate using the Chain Rule:
[tex]y=\cos^2(\frac{x^2 + 2}{x^2 - 2})[/tex]
Homework Equations
The Attempt at a Solution
[tex]y' = -2\cos(\frac{x^2 + 2}{x^2 - 2})\sin(\frac{x^2 + 2}{x^2 - 2}) [\frac{2x(x^2 - 2) - (x^2 + 2)2x}{(x^2 - 2)^2}][/tex]
[tex]\mbox{derivative of cos is -sin so I brought the negative to the front}[/tex]
[tex]y' = -2\cos(\frac{x^2 + 2}{x^2 - 2})\sin(\frac{x^2 + 2}{x^2 - 2}) [\frac{2x(x^2 - 2 - x^2 - 2)}{(x^2 - 2)^2}][/tex]
[tex]y' = -2\cos(\frac{x^2 + 2}{x^2 - 2})\sin(\frac{x^2 + 2}{x^2 - 2})[\frac{-8x}{(x^2 - 2)^2}][/tex]
[tex]y' = 16x(x^2 - 2)^{-2} \cos(\frac{x^2 + 2}{x^2 - 2})\sin(\frac{x^2 + 2}{x^2 - 2})[/tex]
However the worksheet says the answer is:
[tex] y' = 8x(x^2 - 2)^{-2} \sin(\frac{2x^2 + 4}{x^2 - 2})[/tex]
What the *flat line* did I do wrong? My answer isn't even close.
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