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amy0799

  • one year ago

consider the following function. f(x) = sqrt(9-x^2) Find the derivative from the left at x = 3. Find the derivative from the right at x = 3.

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  1. thadyoung
    • one year ago
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    find the derivaite, use chain rule, and then plug in 3 for every x

  2. amy0799
    • one year ago
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    can you show me how?

  3. ChillOut
    • one year ago
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    Let \(u=sqrt(v)\) and \(v=9-x²\). What does the chain rule tells you?

  4. ChillOut
    • one year ago
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    tell*

  5. ChillOut
    • one year ago
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    \(\frac{d}{dx}f(g(x))=f'(g(x))*g'(x))\)

  6. Castiel
    • one year ago
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    Make it simpler yourself by writing \[(9-x ^{2})^{\frac{ 1 }{ 2 }}\] Now you could use that derivation rule \[\frac{ d }{ dx }x ^{n}= nx ^{n-1}\] after that you still have to multiply it with derivation of \[\frac{ d }{ dx}(9-x ^{2})\]

  7. amy0799
    • one year ago
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    would it be 9-2x?

  8. Castiel
    • one year ago
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    \[\frac{ d }{ dx }(9-x ^{2})\] =\[\frac{ d }{dx }9-\frac{ d }{dx }x ^{2}\] Now what is a derivative of a constant number like 9 here?

  9. amy0799
    • one year ago
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    0

  10. Castiel
    • one year ago
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    that means \[\frac{ d }{ dx }(9-x ^{2}) = -2x\]

  11. amy0799
    • one year ago
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    so then how do i find the derivative from the left and right at x=3?

  12. Jhannybean
    • one year ago
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    \[\lim_{x\rightarrow 3^{-}} (9-x^2)^{1/2}\]\[\lim_{x\rightarrow 3^+} (9-x^2)^{1/2}\]

  13. amy0799
    • one year ago
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    do i just plug in 3 for both equation?

  14. amy0799
    • one year ago
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    @ChillOut can you help me

  15. triciaal
    • one year ago
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    |dw:1440964454314:dw|

  16. amy0799
    • one year ago
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    how do i find the derivative from the left and right at x=3?

  17. triciaal
    • one year ago
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  18. triciaal
    • one year ago
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    from the left let x = -3 from the right let x = 3

  19. amy0799
    • one year ago
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    i got the answer wrong

  20. triciaal
    • one year ago
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    why

  21. amy0799
    • one year ago
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    i dont know...

  22. triciaal
    • one year ago
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    didn't you put 0?

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