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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    is it \[8\div(\sqrt{x+9})\]

  2. anonymous
    • 5 years ago
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    no, I dont have that option...

  3. anonymous
    • 5 years ago
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    no is that what you are asking

  4. anonymous
    • 5 years ago
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    oh, in the denominator, x+9 is squared

  5. anonymous
    • 5 years ago
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    oh squared not square root

  6. anonymous
    • 5 years ago
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    yeap

  7. anonymous
    • 5 years ago
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    well just taking the derivative it should be -16/(x+9)^3

  8. anonymous
    • 5 years ago
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    step 1: lim h--> 0 [8/(x+h+9)^2 - 8/(x+9)^2]/h

  9. anonymous
    • 5 years ago
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    factor the top, and cancel out all the terms, you should have a factor of "h" in every term in the numberator

  10. anonymous
    • 5 years ago
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    it's tedious.. but i simplify to ...

  11. anonymous
    • 5 years ago
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    when i factor the denominator, i gont get an h in every term

  12. anonymous
    • 5 years ago
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    -8(2xh+18h+h^2)/[h*((x+h+9)^2)(x^2+18x+81)]

  13. anonymous
    • 5 years ago
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    cancel the h, you get -8(2x+18+h)/[((x+h+9)^2)(x^2+18x+81)]

  14. anonymous
    • 5 years ago
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    in the limit as h--> , this reduces to -16x/(x+9)^3

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