Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

rishi94

  • 2 years ago

y=e^e^x find y'

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

    y' = u' e^u = e^x * e^(e^x)

  2. rishi94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    xe^ex?

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

    NO

  4. rishi94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can u go through the steps? i dont get it.

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

    The formula: y' = u' e^u

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

    u = e^ --> u' = ??

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

    Then just plug it into the formula :)

  8. rishi94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i dont get it..

  9. rishi94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    mind going thru the steps?

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

    In differentiating a function that contains another function (or a series of functions for some), you apply the chain rule. Actually, you perform the chain rule when you differentiate and differentiate the different layers of functions until you reach a point when you are differentiating the most basic function x and you just get 1. To get the y' of e^e^x, we should note that the first layer is e^x where x here is e^x. The deriv of e^x = e^x, so the deriv of the first layer is e^x, but since x here is e^x, we make it e^(e^x). Now for the second layer, it's just e^x where x here is still x. So the deriv of the second layer is e^x where x is x. Now for the third layer, the function is just x, and its deriv is just 1. This is where we stop. Deriv of first layer: e^(e^x) Deriv of second layer: e^x Derive of third layer: 1 (stopped here) Then we just multiply everything, as this is what the chain rule states. So the derivative of the e^(e^x) = (e^(e^x))(e^x)(1) or simply (e^(e^x))(e^x).

  11. rishi94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    where did u get the second layer as e^x as?

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

    Because usually it is just e^x, right? That's the most basic form of that function. In this case, however, e was raised to another e^x, which is another function in itself. That's the second layer.

  13. rishi94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then what is the first layer?

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

    The first layer is e^(e^x) as a whole. The second layer is the e^x inside the first layer (the power).

  15. rishi94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok

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

    Is it clear already? :)

  17. rishi94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    somewhat...

  18. 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.