Derivative of an expoential within an exponential

sprint

[SOLVED] derivative of an expoential within an exponential

help. i need help on finding the derivative of an exponential within an exponential

1. The problem statement, all variables and given/known data

d/dx of e^(e^4x)

2. Relevant equations

d/dx of e^(e^4x)

3. The attempt at a solution

d/dx of e^(e^4x)

i don't know how to attempt this cause the function im interested is in the power of e

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hotcommodity

We know that the derivative of an exponential is simply the exponential times the derivative of power term, right?

$$\frac{d}{du} e^u = e^uu'$$

You're going to have to apply the chain rule.

Does that help?

sprint

We know that the derivative of an exponential is simply the exponential times the derivative of power term, right?

$$\frac{d}{du} e^u = e^uu'$$

You're going to have to apply the chain rule.

Does that help?
i think we are not looking at the same problem. my problem is an exponential within an exponential

d/dx e^(e^4x)

hotcommodity

It's not the exact equation that you need to apply, but that's where you start. If I let $$u = e^{4x}$$, then I must first find the derivative of $$e^u$$.

I know $$\frac{d}{du} e^u = e^uu'$$.

So you know what "u" is, now you must find the derivative of "u" and plug it into the above equation.

sprint

oooooh.

i see. i guess just use substitution letting u = e^(4x)

by any chance, is the correct answer 4e^(4x) times e^(4x) = 4e^(8x)

?

hotcommodity

Not quite, you want to think of "u" as separate from everything else and only plug it in at the end. If $$u = e^{4x}$$, what's the derivative, u' ?

sprint

thats exactly what i did. i made "u" separate.

and the derivative of u is 4e^(4x), to answer your question.

hotcommodity

Right, so you'd have $$4e^{e^{4x}}e^{4x}$$. I didn't see you type in the $$e^{e^{4x}}$$ part.

sprint

wow. totally confusing.

but i think the answer is what i stated earlier...

4e^(4x) times e^(4x)

i get this by sticking to the basics and using the chain rule and substitution

Last edited:

hotcommodity

I'm not trying to confuse you, haha, but I'd hope that you walk away from this understanding what's going on. Let's say I wanted to find the derivative of $$e^{e^x}$$. I'd use the chain rule once again letting $$u = e^x$$. So I'd have:

$$\frac{d}{du} e^u = e^uu'$$

Find u':

$$u' = e^x * 1$$

And plug u and u' into the first equation to get the derivative:

$$e^{e^x}*e^x*1$$

Right?

sprint

check it. i was wrong. the answer should be

4e^(4x) times e^(e^(4x))

which is

u' times e^u

via the chainrule

sprint

I'm not trying to confuse you, haha, but I'd hope that you walk away from this understanding what's going on. Let's say I wanted to find the derivative of $$e^{e^x}$$. I'd use the chain rule once again letting $$u = e^x$$. So I'd have:

$$\frac{d}{du} e^u = e^uu'$$

Find u':

$$u' = e^x * 1$$

And plug u and u' into the first equation to get the derivative:

$$e^{e^x}*e^x*1$$

Right?
i follow you. you are right.

sprint

and how do you type in the equations like that? it looks clean...

hotcommodity

Haha, you just use the "tex" tags. You can click on the equation itself to see how you would type it in. I think there's a tutorial somewhere here on the site.

ok. thanks. lol.

hotcommodity

You're quite welcome :)

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