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Expert: - 10/30/2005


Question
find the derivatives of y with respect to x, t, or theta, as appropriate.

1) y= (1 + ln t)/(t)
2) y= (x ln x)/(1+ln x)

Answer
1)

Use the quotient rule:

y' = [(t)(1+lnt)' - (1+lnt)t']/t^2

y' = [ (t)(1/t) - (1+lnt)]/t^2

y' = [ 1 - 1 - lnt ]/ t^2

y' = -lnt/t^2


2)

Again use the quotient rule:

y' = [(1+lnx)(xlnx)' - (xlnx)(1+lnx)']/(1+lnx)^2

y' = [(1+lnx)(1+lnx) - (xlnx)(1/x)]/(1+lnx)^2

y' = [(1+lnx)^2 - lnx ]/(1+lnx)^2

y' = 1 - lnx/(1+lnx)^2  

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