A function `f` satisfies the condition `f(x)=f^(prime)(x)+f''(x)+f'''(x)....+infinity ,w h e r ef(x)` is a differentiable function indefinitely and dash denotes the order of derivative. If `f(0)=1,t h e nf(x)` is `e^(x/2)` (b) `e^x` (c) `e^(2x)` (d) `e^(4x)`

Options

A. `e^(x//2)`
B. `e^(x)`
C. `e^(2x)`
D. `e^(4x)`

Explanation

To solve the problem, we start with the given condition for the function \( f \):

\[ f(x) = f'(x) + f''(x) + f'''(x) + \ldots \]

### Step 1: Rewrite the equation
We can express the right-hand side in terms of \( f \) and its derivatives.
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