How to Differentiate e^e^x ?

What is the derivative of e^e^x? This is a composite function, so we apply the chain rule to take the derivative of e^e^x. By applying the chain rule, we first differentiate the whole function without changing the inner function. Then, multiply it by the derivative of the inner function. In other words, when we are trying to take the derivative of an exponential function using the chain rule, we first copy back the whole function exactly, and multiply it by the derivative of its exponent. That is the reason we got ( e^e^x * e^x ) for the derivative, so we ended up with e^(e^x + x).
CHAIN RULE EXPLANATION VIDEO: → • Learn Chain Rule Diffe...
DERIVATIVE OF e^x: → • How to Differentiate e^x?
TIMECODES:
0:00 → Intro
0:18 → e^e^x is a Composite Function
0:35 → Apply the Chain Rule
1:11 → Rewrite the Expression
1:30 → Review
1:42 → We did it!

[@eustacenjeru7225]

Great

[@izzyqrz1]

You can also do it with implicit differentiate
As ln y =ln(e^e^×) , so that properties of log/natural log you get ln y = e^xln(e) where ln(e) is 1 then differentiate both sides and you get the same thing

[@YeahMathIsBoring]

Yes, this is an alternative way to find the derivative using implicit differentiation and we will still be getting the same answer. Nice one! 👍

[@devilspattern6164]

Chain rule

[@victor1978100]

How to differentiate x^e^x ?

[@victor1978100]

(e^x)*(x^e^x)*(1/x+lnx)