A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Find y' assuming that the equation determines a differentiable function f such that y= f(x) sin^2 3y=x+y-1

  • This Question is Closed
  1. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(sin^2(3y)\) ??

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

    its implicit differentiation

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah; but whats the equation?

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

    yes amistre that is correct

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

    its kind of assumed its sin^2 (3y) lol

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

    its unlikely to be sin^2(3) y

  7. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[3y' 2\cos(3y)=1+y'\] \[6y'\cos(3y)-y'=1\] \[y'(6\cos(3y)-1)=1\] \[y' = \frac{1}{6\cos(3y)}\]

  8. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thats wrong ....

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

    ?

  10. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i did sin^2(3y) as tho it was simply sin(3y)

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

    ohh yeh, I see

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

    alot of chain rules in that question

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

    its only once elecengineer

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

    lol

  15. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[3y'.2(\sin(3y)).cos(3y)=1+y'\] \[y'.6\sin(3y)\cos(3y)-y'= 1\] \[y'(6\sin(3y)\cos(3y)-1)= 1\] \[y' = \frac{1}{6\sin(3y)\cos(3y)-1}\] maybe

  16. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    3 times actually

  17. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[u^2.sin(v).3y\]

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

    also, you couls apply double angle formula for sin to simplify the bottom :P

  19. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup

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

    im trying to figure out what you did amistre

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

    consider the LHS first, the derivative of the RHS is easy as

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

    so ( sin(3y) )^2 apply the chain rule , bring the power down in front , leave the inside of the bracket alone , reduce the power by one , then multiplt by the derivative of the inside

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

    so d/dx [ (sin(3y) ) ^2 ] = 2 sin(3y) [d/dx ( sin(3y) ) ]

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

    = 2 sin(3y) 3y' cos(3y)

  25. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    say you wanna derive: u^2; thats simple right? but: u = sin(v) and v = 3y

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

    when you differentiate sin(3y) you take the derivative of the inside with respect to x, and then change the sin function to a cos function

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

    the derivative of 3y with respect to x is 3 (dy/dx) = 3y'

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

    i get the 2(sin3y)(cos y) but not the 3y'

  29. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[{du\over dx}={du\over dv}{dv\over dy}{dy\over dx}\] \[\frac{d(sin^2(3y))}{dx}=2sin(3y)*cos(3y)*3y'\]

  30. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you dont understand why we keep something hta tyou were taught to throw out

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

    :S?

  32. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[y = 2x^3 \rightarrow y' = 6x^2 x'\]

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

    oh...

  34. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what did the \(y\) derive to? \(y'\) right?

  35. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    3y derives to: \(3 y'\) \(5y^2\) derives to \(10y .y'\)

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

    so the derivative of sin 3y is 3 sin 3y then 3y' cos 3y?

  37. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you are used to throwing out the x' bit; but that is only because \(dx\over dx\)=1

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

    i know that ist the trig function thats throwing me off

  39. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sin(3y) derives to 3y' cos(3y)

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

    yes...thats what confused me or should i say confuses

  41. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the sin to cos? or the innards to the outside?

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

    the innards the 3y inside the sin 3y

  43. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the innards have a controling part in the function and have to be accounted for. They are the driving force that produces the output for the sin function

  44. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the 'chain' rule is just accounting for all the inputs and outputs thru the equation that eah have a controling part

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

    ok i guess i have to practice some more examples of them

  46. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    try it on simple ones first: like, compound functions

  47. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    interactmath.com can help; its a free practice math site

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

    THANKS AGAIN SO MUCH AMISTRE AND ELECENGINEER

  49. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    youre welcome :)

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

    can you help me with the question i posted earlier today

  51. 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.