y=e^e^x
find y'

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

- anonymous

y=e^e^x
find y'

- chestercat

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

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

- anonymous

xe^ex?

- anonymous

NO

Looking for something else?

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

## More answers

- anonymous

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

- anonymous

The formula:
y' = u' e^u

- anonymous

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

- anonymous

Then just plug it into the formula :)

- anonymous

i dont get it..

- anonymous

mind going thru the steps?

- anonymous

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).

- anonymous

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

- anonymous

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.

- anonymous

then what is the first layer?

- anonymous

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

- anonymous

oh ok

- anonymous

Is it clear already? :)

- anonymous

somewhat...

Looking for something else?

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