Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

rishi94

  • 4 years ago

y=e^e^x find y'

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

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

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

    xe^ex?

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

    NO

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

    The formula: y' = u' e^u

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

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

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

    Then just plug it into the formula :)

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

    i dont get it..

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

    mind going thru the steps?

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

    then what is the first layer?

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

    oh ok

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

    Is it clear already? :)

  17. rishi94
    • 4 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

Sign Up
Find more explanations on OpenStudy
Privacy Policy