`y = e^(e^x)` Find y' and y''

Textbook Question

Chapter 3, 3.4 - Problem 50 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsenviro | College Teacher | (Level 1) Educator Emeritus

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`y' = d/dx e^(e^x)`

`= e^(e^x) * d/dx(e^x) = e^(e^x)*e^x`

`y'' = d/dx(e^(e^x)*e^x)`

`= d/dx(e^(e^x)) * e^x + e^(e^x) *d/dx e^x`

`= e^(e^x)*e^(2x) + e^x*e^(e^x)`

`= e^(e^x)*e^x (e^x +1)`

``hope this helps.

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