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avai70178

  • one year ago

Someone please help. I understand the chain rule for derivatives but i'm not sure how to use it in this problem. y=(x^2+1)(x+1)^2

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  1. Loser66
    • one year ago
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    It is not a chain rule, it is product rule. Where are you stuck?

  2. avai70178
    • one year ago
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    I'm not sure if I should use the product rule on both pieces of the equation with the same exponent.

  3. Loser66
    • one year ago
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    Let a = x^2 +1 then a' = ? Let b = (x+1)^2 , then b' =?

  4. avai70178
    • one year ago
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    a= 2 b=2x+2

  5. Loser66
    • one year ago
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    no, not that a' = 2x, b' is ok.

  6. Loser66
    • one year ago
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    ok, now. y = a*b , then y' = a'b + b'a ok?

  7. avai70178
    • one year ago
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    oops sorry i didnt mean to post that

  8. avai70178
    • one year ago
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    wait well what is a then?

  9. avai70178
    • one year ago
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    if we are using the product rule than a should equal just 2

  10. Loser66
    • one year ago
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    is it not that we defined a = x^2 +1? and b = (x+1)^2??

  11. avai70178
    • one year ago
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    yes and if we take the derivatives of those then we have a'=2 and b'=?

  12. Loser66
    • one year ago
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    I think you got confuse. ok, let me walk you through the concept. Answer me one by one ok? (x) ' =?

  13. avai70178
    • one year ago
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    do you mean derivative of x? cause idk

  14. Loser66
    • one year ago
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    yes, derivative of x =?

  15. avai70178
    • one year ago
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    idk

  16. avai70178
    • one year ago
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    im sorry i feel dumb

  17. Loser66
    • one year ago
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    ok, I tell you x' =1 \((x^\color{red}{2})' =\color{red}{2}x^1= \color{red}{2}x\) \((x^\color{red}{3})' =\color{red}{3}x^2\) \((x^\color{red}{5})' =\color{red}{5}x^4\) Now, tell me \((x^{10})' =?\)

  18. avai70178
    • one year ago
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    10x^9

  19. Loser66
    • one year ago
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    Good, that is called "n-rule" , ok?

  20. avai70178
    • one year ago
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    ok

  21. Loser66
    • one year ago
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    One more thing you should know, derivative of a constant =0, that is (3)' =0 5' =0 10'=0 tell me (234)' =?

  22. avai70178
    • one year ago
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    0

  23. Loser66
    • one year ago
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    good!! Now, combine them \((x +y) ' = x' +y' \) \((x^2 +5)' = (x^2)' +5' =???\)

  24. avai70178
    • one year ago
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    2x?

  25. Loser66
    • one year ago
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    yup

  26. Loser66
    • one year ago
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    now, product rule: (x*y)' = x'*y + y' *x ok?

  27. avai70178
    • one year ago
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    yes

  28. Loser66
    • one year ago
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    Now, Your problem : \(((x^2+1) *(x+1)^2)' \)

  29. Loser66
    • one year ago
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    apply product rule, right? what do you get?

  30. avai70178
    • one year ago
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    8x+4

  31. avai70178
    • one year ago
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    i think

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