Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

lovesit2x

  • 2 years ago

Find (d^(2)y)/(dx^(2)) for the following function. y=e^(-4x^(2))

  • This Question is Closed
  1. abb0t
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So find the second derivative of the function.

  2. abb0t
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    This requires that you use the chain rule.

  3. lovesit2x
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[Find \frac{ d ^{2}y }{ dx ^{2} } for the following function. y=e ^{-4x ^{2}}\]

  4. abb0t
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    First, start by using chain rule. For the second derivative, you will be using product rule AND chain rule.

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

    You want \[\frac{d}{dx}\left( \frac{dy}{dx}\right)\]

  6. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    first derivative is \[-8xe^{-4x^2}\] by the chain rule second derivative requires the product rule

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

    Do you understand how Sat got that first derivative? c:

  8. abb0t
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes. I do.

  9. lovesit2x
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

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

    \[\large y'=-8xe^{-4x^2}\] So now you need to find the second derivative as was stated above. \(\large y''\) To differentiate this a second time, you'll need to apply the Product Rule, very similarly to the way we did it in the last problem! :)

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

    Fine fine fine D: I'll do the pretty colors like last time. Maybe that will help.

  12. lovesit2x
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol

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

    \[\huge y''=\color{royalblue}{\left(-8x\right)'}e^{-4x^2}-8x\color{royalblue}{\left(e^{-4x^2}\right)'}\]Product Rule setup for the second derivative. The second blue term should give you the same thing you got for the first derivative!

  14. lovesit2x
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    omg, its that easy??? why am i overthinking this

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

    :3

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

    What do you get for the first set of blue brackets?

  17. lovesit2x
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -8

  18. lovesit2x
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    n the second is the -8x e ^-4x^2

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

    \[\huge y''=\color{orangered}{\left(-8\right)}e^{-4x^2}-8x\color{orangered}{\left(-8xe^{-4x^2}\right)}\] Like that? Yay good job!

  20. lovesit2x
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i love that lol

  21. 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.