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marytheshade Group Title

I need to find the derivative using the chain and quotient rules of F(x)= ((3x-2)^3)/((x-3)^5). I just don't know when to stop doing chain rule and start the quotient

  • one year ago
  • one year ago

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  1. frx Group Title
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    Start by thinking of the quotient rule, it's (f'(x)g(x)-f(x)g'(x))/(g(x))^2

    • one year ago
  2. frx Group Title
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    Then you just replace the derivitives using the chainrule

    • one year ago
  3. frx Group Title
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    \[\frac{ f'(x)*(x-3)^{5} - (3x-2)^{3}g'(x) }{(x-3)^{10} }\]

    • one year ago
  4. marytheshade Group Title
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    don't you have to do the chain rule first? is it possible to derive the F(x) and g(x) equations without the chain rule?

    • one year ago
  5. frx Group Title
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    You have to do the chainrule when replacing the derivitives in the function i wrote above

    • one year ago
  6. frx Group Title
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    I think it's easier to start of writing it as above

    • one year ago
  7. marytheshade Group Title
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    okay so I did the chain rule and got F'(g(x))= 9(3x-2)^2 (top function deriv) and g'(x)= 5(x-3)^4 (denominator deriv) so do I plug in those values or do I have to take the chain rule further?

    • one year ago
  8. frx Group Title
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    You just put them in as you counted them, the derivitive of f(x) is f'(x) and it's what you're looking for according to the quotientrule.

    • one year ago
  9. Chlorophyll Group Title
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    You've done with derivative u' and v' Plug them into the formula ( u'v - uv' ) / v²

    • one year ago
  10. marytheshade Group Title
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    Thank you!!

    • one year ago
  11. frx Group Title
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    np

    • one year ago
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