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Unformatted text preview: Example
π Find y (x) if y (x) = (ln x2 ) .
If we ﬁrst note that y = f (g (x)), where f (x) = xπ and g (x) = ln x2 , then by chain rule
dy
= f (g (x))g (x).
dx
For this problem, f (x) = πxπ−1 and g (x) = 2x
, thus
x2 dy
= π ln x2
dx π −1 2
·.
x ...
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.
 Fall '10
 KIHYUNHYUN
 Calculus, Chain Rule

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