anonymous
  • anonymous
differentiate y = x^3(1+x)^3
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
u = x^3 u' = 3x^2 v = (1+x)^3 v'=3(1+x)^2 y' = u'v + uv'
anonymous
  • anonymous
use product rule
anonymous
  • anonymous
so what would you get as an answer

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anonymous
  • anonymous
what answer did you get?
anonymous
  • anonymous
combine all to y'
anonymous
  • anonymous
i got 3x^2(1+x)^3 + 3x^3(1+x)^2
anonymous
  • anonymous
thats true
anonymous
  • anonymous
but the solutions at the end of the text book say that the answer is 3x^2(1+x)^2(1+2x)
anonymous
  • anonymous
so ???
anonymous
  • anonymous
You can do it the long way and evaluate \[(1+x)^3 = 1+3x+ 3x^2+ x^3 \] Then multiply it with \[x^3\] and simply differentiate
anonymous
  • anonymous
oh ok thank you romero! =D
anonymous
  • anonymous
I mean its tedious and there are other ways that are much easier but you can always do that. I recommend learning substitution. You will come upon problems where simply evaluating will not work.
anonymous
  • anonymous
ohhhh like that, sorrry cant help much
anonymous
  • anonymous
oh ok a BIG THANKS to all!

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