Differentiate `e^(sqrt(tanx))` from first principles

Explanation

To differentiate \( e^{\sqrt{\tan x}} \) from first principles, we will follow the definition of the derivative:

\[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]

where \( f(x) = e^{\sqrt{\tan x}} \).

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