Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

amonoconnor

  • one year ago

When using the Chain Rule, and taking the second piece of derivative (dy/dx of the term for "theta"), would this be correct... (?) In my particular situation: The "theta" = (1/y) So... Because it's not the first step in the chain rule, and I'm "re-deriving" as my math teacher says, the constant (1) is affectable. So... Is the following derivation correct? 1/y = (0)/[y^(1-1)(dy/dx)] = 0/y^(0)(dy/dx) = 0/(1)(dy/dx) = 0/(dy/dx) = (0)

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

    @agent0smith Yes... I know. I'm a thorn in your side ;)

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

    "theta" = (1/y) ?? I don't understand :(

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

    Yep, in he function I'm taking the derivative of, the quantity "1/y" is in the "inside" spot, in Chain Rule terminology, or the spot of theta in regard to the trig function also in the function. I have taken the derivative of the whole "outside", finding the derived/ new trig function (theta term untouched), but now I must take the derivative of the theta term itself, and multiply that by the first part; to complete the derivation process, and find the final answer. I'm just wondering if this is in fact the right derivative. :)

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

    Ok so for the derivative of the inner function (1/y), You're thinking you get zero for some reason? Did you apply the quotient rule or power rule or something?

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

    My problem: "ySIN(1/y) = 1 - xy"; Find dy/dx. ( Thought this would be helpful to see)

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

    Umm, no.... I should have, shouldn't I have though? Used the quotient rule?

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

    You can rewrite it like this:\[\Large \frac{1}{y}\quad=\quad y^{-1}\]And apply the power rule as you normally would. I'm not quite sure where your 0 is coming up in the denominator. If you use the quotient rule you should get something like:\[\Large \frac{0y-1(1)}{y^2}\]

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

    the zero in the numerator, i meant to say :)

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

    Oh and a \(\Large y'\) should show up when you chain again.

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

    But it looks like you understood that part :o i see your dy/dx in there somewhere (although it shouldn't be in the denominator XD heh )

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

    The "Power Rule"? I'm not familiar with that... This is what we learned in Calc, at least from my teacher: (?) y' = (y^(1-1))*(dy/dx) = (y^(0))*(dy/dx) = (1)*(dy/dx) = dy/dx

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

    Is that a y to the first power on the left there?

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

    Y prime

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

    You've learned about the chain rule before the power rule...?\[\Large \frac{d}{dx}x^n\quad=\quad n x^{n-1}\]That doesn't look familiar? +_+

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

    Oh... Yes, I know of that. Whoops! I guess we don't know the terminology... I will bring that up to him!

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

    Ahhhh, I follow your post from earlier... :)

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

    Using rules of exponents allows us to write the inner function like this:\[\Large \frac{1}{y}\quad =\quad y^{-1}\]From here we don't need to use the quotient rule, we use the power rule instead:\[\Large \frac{d}{dx}y^{-1}\quad=\quad -1y^{-1-1}\frac{dy}{dx}\quad=\quad -y^{-2}\frac{dy}{dx}\]

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

    Alright.... You're so amazing. I do believe I'm good now. I have what I need, and most importantly, I fully understand what happened, and what I need to do. Thank you so much!

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

    (Would you mind medaling me?)

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

    oh got it from there? cool c:

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

    Yep, I do! Thanks you so much again; you really helped me look at that from a better angle.

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.