Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

calculushelp01 Group Title

derivative of sqrt x + (1/4) sin (2x)^2

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. kelly226 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If the square is meant for the sin... y = sqrt x + (1/4)[sin 2x]^2 y' = (1/2)(1 / sqrt x) + (1/4)(2)(sin 2x)(cos 2x)(2) = (1 / 2 sqrt x) + (sin 2x)(cos 2x)

    • 2 years ago
  2. kelly226 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If the square is only on the 2x... y = sqrt x + (1/4)sin (2x)^2 = sqrt x + (1/4) sin (4x^2) y' = (1/2)(1 / sqrt x) + (1/4)[cos (4x^2)](4*2x) = (1 / 2 sqrt x) + (2x)cos (4x^2)

    • 2 years ago
  3. RadEn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    hint : derivative of sqrt(f(x)) = 1/(f'(x)*sqrt(f(x)) and derivative of sin(g(x))=g'(x)*cos(g(x))

    • 2 years ago
  4. calculushelp01 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    could you step by step for the solution (the square is only on the 2x)

    • 2 years ago
  5. kelly226 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    If the square is only on the 2x... y = sqrt x + (1/4)sin (2x)^2 = sqrt x + (1/4) sin (4x^2) y' = (1/2)(1 / sqrt x) + (1/4)[cos (4x^2)](4*2x) = (1 / 2 sqrt x) + (2x)cos (4x^2)

    • 2 years ago
  6. RadEn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @kelly226 is right

    • 2 years ago
  7. calculushelp01 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    is the the (2x)^2 becoming (2x^2) product rule?

    • 2 years ago
  8. kelly226 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont think so...

    • 2 years ago
  9. RadEn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    its use chain rule... derivative of (2x)^2 is 2(2x)*2

    • 2 years ago
  10. calculushelp01 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wouldnt the derivative of (2x)^2 be 4x then according to chain rule= 2(2x)^2-1 (2)

    • 2 years ago
  11. RadEn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    2(2x)*2=8x not 4x

    • 2 years ago
  12. RadEn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but, if we look the first question there is a coefficien of sin (2x)^2 (is 1/4), so multiply it by derivative of sin (2x)^2

    • 2 years ago
  13. RadEn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    therefore, 1/4*2(2x)*2*cos(2x)^2 = 2xcos(2x)^2

    • 2 years ago
  14. calculushelp01 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I understand the 2xcos part of the solution. But I dont understand why the original (2x)^2 remains

    • 2 years ago
  15. RadEn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    because derivative of sin(f(x) is f'(x)*cos(f(x))

    • 2 years ago
  16. calculushelp01 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okay thank you very much

    • 2 years ago
  17. RadEn Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wellcome :)

    • 2 years ago
    • Attachments:

See more questions >>>

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.