If `y=f(a^x)a n df^(prime)(sinx)=(log)_e x ,t h e nfin d(dy)/(dx),` if it exists, where `pi/2

Explanation

To solve the problem step by step, we start with the given information and apply differentiation rules accordingly.

### Step-by-Step Solution

1. **Given Information**:
We have \( y = f(a^x) \) and \( f'(\sin x) = \log_e x \).

2. **Differentiate \( y \) with respect to \( x \)**:
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