`Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4),` then find the value of `f^(prime)(2)`

Explanation

To solve the problem, we need to find the value of \( f'(2) \) given that \( f(x) = e^{g(x)} \) and \( g(x) = \int_2^x \frac{t}{1+t^4} dt \).

### Step-by-Step Solution:

1. **Differentiate \( f(x) \)**:
\[ f'(x) = \frac{d}{dx} e^{g(x)} = e^{g(x)} \cdot g'(x) \]
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