A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Carissa15

  • one year ago

how do I differentiate 4sqrt(u^2+u) ?

  • This Question is Closed
  1. arindameducationusc
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    with respect to u?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    WELCOME TO OPENSTUDY!

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i will help ya :)

  4. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh yes, sorry. It says Differentiate f(u) I have not yet differentiated using roots yet

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol fu

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so first:

  7. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sqrt[4]{u^2+u}\]

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so first of all do you know how to simplify the equation?

  9. arindameducationusc
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    See this......

    1 Attachment
  10. arindameducationusc
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Carissa15 you there?

  11. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, that makes sense so far

  12. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I thought that you add 1/2 to "remove" the root from the equation but then I get lost..

  13. arindameducationusc
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ??

  14. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So you could then take the derivative of the simplified equation? I didn't know how to simplify and remove the \[\sqrt{u}\] from the equation

  15. arindameducationusc
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O....... sqrt=1/2, 4sqrt=4/2=2. Got it?

  16. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cool, thank you :-) much more sense

  17. arindameducationusc
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    My pleasure.... Don't forget to add a medal and be a fan. And definitely ask more questions. Will try my best to help!

  18. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which would leave me with \[4u^2+2(2u+1)+4u\] as the derivative?

  19. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\sqrt[4]{u^2+u} \implies (u^2+u)^{1/4}\] \[\frac{ d }{ du } (u^2+u)^{1/4} = \frac{ 1 }{ 4 }(u^2+u)^{-3/4} \times \frac{ d }{ du }(u^2+u)\] notice we apply the chain rule.

  20. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So your derivative should be \[\frac{ 1 }{ 4 }(u^2+u)^{-3/4} (2u+1)\]

  21. triciaal
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1438235581850:dw|

  22. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Or you can put it as \[\frac{ (2u+1) }{ 4(u^2+u)^{3/4} }\]

  23. triciaal
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    please clarify the original notice @Astrophysics and I did 2 different problems

  24. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\color{blue}{\text{Originally Posted by}}\) @Carissa15 \[\sqrt[4]{u^2+u}\] \(\color{blue}{\text{End of Quote}}\) @triciaal

  25. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, that was the original that I needed to find the derivative of, however I struggle with taking the root when using derivatives.

  26. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just remember your exponent rules if you have trouble with square roots \[\huge \sqrt[n]{x} \implies x^{1/n}\] then you can easily use power rule.

  27. arindameducationusc
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Astrophysics is here... he is really good.... He will take care..... @Carissa15

  28. triciaal
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I see that now in the body but not in the original

  29. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, thanks. Easier to work with powers

  30. triciaal
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Astrophysics did you see the original?

  31. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Alright, so everything is clear now? Another thing, the way they show derivatives for square root for example \[\frac{ d }{ dx } \sqrt{x} = \frac{ 1 }{ 2\sqrt{x} }\] notice they show it as such right? This is the same thing as \[\frac{ d }{ dx } x^{1/2} = \frac{ 1 }{ 2 }x^{-1/2} = \frac{ 1 }{ 2x^{1/2} } = \frac{ 1 }{ 2\sqrt{x} }\] And yes I did @triciaal I could see your confusion, don't worry about it! :)

  32. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So just mess around, and see what you get, that's the best way to learn!

  33. triciaal
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am not confused I read what was posted just as it was posted.

  34. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    when using the power rule, you subtract by 1 (to the power) while multiple the rest of the relevant equation. But when you have fraction powers such as this?

  35. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, it's the same, the power rule is as follow \[\frac{ d }{ dx } x^{n} = nx^{n-1}\]

  36. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    got it. Thank you everyone :-)

  37. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Np

  38. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    got it. Thank you everyone :-)

  39. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.