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Question regarding Higher Derivatives

  1. Oct 29, 2007 #1
    when working with higher derivatives each time we differentiate a polynomial the degree decreases by 1.

    I am asked to find the second and third derivatives of this polynomial: y=(x^4)(e^x)

    I get the following (pretty sure it's right):

    y`= (x^4)(e^x) + 4(x^3)(e^x)

    y`` = (x^4)(e^x) + 8(x^3)(e^x) + 12(x^2)(e^x)

    y``` = (x^4)(e^x) + 12(x^3)(e^x) + 36(x^2)(e^x) + 24(x)(e^x)

    I thought the degree's of the polynomials were supposed to decrease with each differentiation? Isn't each polynomial still degree 4?

    Where is my error :confused:
  2. jcsd
  3. Oct 29, 2007 #2


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    Your derivatives are right. The problem is that you are not dealing with polynomials. The e^x term is exponential, not polynomial, in nature. So, the properties of polynomials do not necessarily apply here, since your polynomial term in the function is multiplied by and exponential term.
  4. Oct 29, 2007 #3
    arg, I guess I was thrown off by the x^4... that made me think I was dealing with a polynomial. I guess I need to review basic algebra to remind myself what a polynomial is:redface:
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