anonymous
  • anonymous
can someone help me do this please? - Using the definition lim h->0 f(x+h) - f(x)/h, to find the derivative at x. f(x)= 8/(x+9)^2
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
is it \[8\div(\sqrt{x+9})\]
anonymous
  • anonymous
no, I dont have that option...
anonymous
  • anonymous
no is that what you are asking

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anonymous
  • anonymous
oh, in the denominator, x+9 is squared
anonymous
  • anonymous
oh squared not square root
anonymous
  • anonymous
yeap
anonymous
  • anonymous
well just taking the derivative it should be -16/(x+9)^3
anonymous
  • anonymous
step 1: lim h--> 0 [8/(x+h+9)^2 - 8/(x+9)^2]/h
anonymous
  • anonymous
factor the top, and cancel out all the terms, you should have a factor of "h" in every term in the numberator
anonymous
  • anonymous
it's tedious.. but i simplify to ...
anonymous
  • anonymous
when i factor the denominator, i gont get an h in every term
anonymous
  • anonymous
-8(2xh+18h+h^2)/[h*((x+h+9)^2)(x^2+18x+81)]
anonymous
  • anonymous
cancel the h, you get -8(2x+18+h)/[((x+h+9)^2)(x^2+18x+81)]
anonymous
  • anonymous
in the limit as h--> , this reduces to -16x/(x+9)^3

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