`f(t) = tan(e^t) + e^(tan(t))` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 39 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsenviro | College Teacher | (Level 1) Educator Emeritus

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Using d/dt (e^t) = e^t and d/dt (tan t) = sec^2 t

`y' = d/dt (tan e^t) + d/dt e^(tan t)`

`= sec^2 (e^t) d/dt e^t + e^(tan t) d/dt (tan t)`

`= e^t sec^2(e^t) + e^(tan t) sec^2 t`

hope this helps.

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