A community for students.
Here's the question you clicked on:
 0 viewing
rishi94
 2 years ago
y=e^e^x
find y'
rishi94
 2 years ago
y=e^e^x find y'

This Question is Closed

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.0y' = u' e^u = e^x * e^(e^x)

rishi94
 2 years ago
Best ResponseYou've already chosen the best response.0can u go through the steps? i dont get it.

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.0The formula: y' = u' e^u

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.0Then just plug it into the formula :)

rishi94
 2 years ago
Best ResponseYou've already chosen the best response.0mind going thru the steps?

imagreencat
 2 years ago
Best ResponseYou've already chosen the best response.0In 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).

rishi94
 2 years ago
Best ResponseYou've already chosen the best response.0where did u get the second layer as e^x as?

imagreencat
 2 years ago
Best ResponseYou've already chosen the best response.0Because 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.

rishi94
 2 years ago
Best ResponseYou've already chosen the best response.0then what is the first layer?

imagreencat
 2 years ago
Best ResponseYou've already chosen the best response.0The first layer is e^(e^x) as a whole. The second layer is the e^x inside the first layer (the power).

imagreencat
 2 years ago
Best ResponseYou've already chosen the best response.0Is it clear already? :)
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.