Expert: Steve Holleran - 8/29/2007

Question
Find the derivative of: y = (X^4/4)(ln X) - (X^4/4) I'm having trouble with this one.  I get an answer of:
(X^3/4)+ln X  The book gives X^3+ln X.  From my work, I see that the first (X^4/4) stayed as is throughout.  But when I manipulate it only, in subsequent attempts, I get answers that are way off.  Thanks for any assistance.

Answer
Hi Ron,

Okay, lets see... You need to use the Product Rule on the first part:

y = (x^4 / 4)(ln x) - (x^4 / 4)

      The stuff in the front of the next line, up to the -
      sign, is the product rule result.

 y' = (x^4 / 4)(1/x) + (ln x)(4x^3 / 4) - (4x^3 / 4)

    = (x^3 / 4) + x^3 * ln x - x^3

    = -3/4 * x^3 + x^3 * ln x

    = x^3 ( -3/4 + ln x)

I've checked my work a couple times, and I don't think I made any mistakes.  

Let me know how this falls out.

Steve Holleran