anonymous
  • anonymous
What is the second derivative of (x^2 +5)^4? I've got the answer, but I don't know how to simplify it.... But my answer may be wrong. I got [8x(x^2 +5)^3] + [ 8(x^2 +5)^4]
Mathematics
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anonymous
  • anonymous
What is the second derivative of (x^2 +5)^4? I've got the answer, but I don't know how to simplify it.... But my answer may be wrong. I got [8x(x^2 +5)^3] + [ 8(x^2 +5)^4]
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
nah, after the first derivative it looks like your product rule went awry
anonymous
  • anonymous
what did you get for the first derivative? 8x(x^2+5)^3???
anonymous
  • anonymous
I'm not surprised... I'm awful at math. :/ I got 8x(x^2 +5) +8

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anonymous
  • anonymous
Oops, make that 8x(x^2 +5)^3 +8
anonymous
  • anonymous
whoops, wrong thread...
anonymous
  • anonymous
umm, nah everybody struggles with calculus the first go round!
anonymous
  • anonymous
ok, for the first derivative, don't add 8 since it is not a product rule. other than that it looks fine
anonymous
  • anonymous
so y'=8x(x^2+5)^3 now to find y'' take derivative of this and use product rule with the first product being 8x and then the second term of the product being (x^2+5)^3
anonymous
  • anonymous
I got [8x * 8x(x^2+5)^3] + [8(x^2+5)^4]
anonymous
  • anonymous
But I have to simplify that (assuming that what I have is right, but it's probably not), which is what I can't figure out. I know that the GCF is 8(x^2+5)^3, and I know that the second half of the equations will be (x^2+5), but the first half is what I don't understand.
anonymous
  • anonymous
derivative of 8x is just 8, so the first term will be 8*(x^2+5)^3 the next term, now instead of differentiating with respect to 8x, you do (x^2+5)^3
anonymous
  • anonymous
which should give you 8x*[6x(x^2+5)^2] or 48x^2(x^2+5)^2
anonymous
  • anonymous
the whole second derivative then will be those two terms added together 8*(x^2+5)^3 +48x^2(x^2+5)^2
anonymous
  • anonymous
But that's not the simplified version, right?
anonymous
  • anonymous
yeah, take out the GCF of 8(x^2+5)^2*[x^2+5+6x^2) and then combine like terms
anonymous
  • anonymous
final answer should be something like y''= 8(x^2+5)^2*(7x^2+5)
anonymous
  • anonymous
I typed that into my assignment, and it says that should be this 8(x^2+5)^3*(7x^2+5)
anonymous
  • anonymous
hmm, let me double-check, but I don't think so, since the power that is common should have dropped down to 2, not 3
anonymous
  • anonymous
hmm, I got the same answer when I re-did it...I don't know why it is a power of 3 to be honest
anonymous
  • anonymous
I don't, either! :p Thanks for helping me, though! I really appreciate it! :)

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