Expert: Paul Klarreich - 8/17/2011

Question
hi, i cannot seem to understand how to get the second derivative for this sum.
y= x+2/x-3 then d^2y/dx^2

so i did first differentiation

y'= (x)(x-3)-(x+2)(x)/(x-3)^2

im confused about the second differentiation, do i just simply use the normal product rule again... this is what i got so far

y"= -5x(x-3)^2-((/5x)(2x)2x(x-3))/(x-3)^4
am i correct so far
please help me??

Answer
Questioner:AYESHA
Country:KwaZulu-Natal, South Africa
Category:Calculus
Private:No
Subject:calculus differentiation
Question:

hi, i cannot seem to understand how to get the second derivative for this sum.
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>>>> this is not a sum.  It is a quotient.  Be careful about using mathematical vocabulary.  Careless use of vocabulary is a good way to fail in math.
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y= x+2/x-3 then d^2y/dx^2

so i did first differentiation

y'= (x)(x-3)-(x+2)(x)/(x-3)^2  <<<<  WRONG.  Review the quotient rule.

Should be:
    (x-3)(1) - (x+2)(1)
y' = --------------------  <<< which you should simplify
         (x-3)^2

im confused about the second differentiation, do i just simply use the normal product rule again... this is what i got so far

y"= -5x(x-3)^2-((/5x)(2x)2x(x-3))/(x-3)^4
am i correct so far

>>>>>>>>> No.

please help me.
.....................................

    x + 2
y = -------
    x - 3

    x - 3 + 5
y = ----------   <<  trick
    x - 3

         5
y = 1 +  -------   <<  trick
         x - 3

 
y = 1 +  5(x - 3)^-1

y' = - 5(x - 3)^-2  << which you get if you simplify your Q-R answer.

Now it will be easy to find  y''.