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

Explanation

To solve the problem, we need to find \(\frac{dy}{dx}\) given that \(y = f(a^x)\) and \(f'(\sin x) = \log_e x\) for \(\frac{\pi}{2} < x < \pi\).

### Step-by-Step Solution:

1. **Identify the given information**:
- We have \(y = f(a^x)\).
- We know that \(f'(\sin x) = \log_e x\).

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