Calculus Help?

I need help checking a homework problem. Could someone tell me the first and second derivatives of e^(x-1)/(x-1)

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A few days ago

Anonymous

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1st. derivative:

[ (x – 1)e^(x – 1) – e^(x – 1) ] / (x – 1)^2

= (x – 2)e^(x – 1) / (x – 1)^2.

2nd. derivative:

{ (x – 1)^2 [ (x – 2)e^(x – 1) + e^(x – 1) ]

– (x – 2)e^(x – 1) 2(x – 1) }

/ (x – 1)^4

= [ (x – 1)^2 – 2(x – 2) ] e^(x – 1) / (x – 1)^3

= (x^2 – 2x + 1 – 2x + 4)e^(x – 1) / (x – 1)^3

= (x^2 – 4x + 5)e^(x – 1) / (x – 1)^3.

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