`f_n(x)=e^(f_(n-1)(x))` for all `n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)}` is (a)`(f_n(x)d)/(dx){f_(n-1)(x)}` (b) `f_n(x)f_(n-1)(x)` (c)`f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x)` (d)none of these

Options

A. `f_(n)(x)(d)/(dx){f_(n-1)(x)}`
B. `f_(n)(x)f_(n-1)(x)`
C. `f_(n)(x)f_(n-1)(x)...f_(2)(x).f_(1)(x)`
D. None of these

Explanation

To solve the problem, we need to differentiate the function \( f_n(x) = e^{f_{n-1}(x)} \) with respect to \( x \), where \( f_0(x) = x \).

### Step-by-step Solution:

1. **Identify the Function**:
We have \( f_n(x) = e^{f_{n-1}(x)} \) and \( f_0(x) = x \).

2. **Differentiate \( f_n(x) \)**:
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