Find `(dy)/(dx),w h e n` `x=e^(theta)(theta+1/theta)a n dy=e^(-theta)(theta-1/theta)`

Explanation

To find \(\frac{dy}{dx}\) when \(x = e^{\theta} \left(\theta + \frac{1}{\theta}\right)\) and \(y = e^{-\theta} \left(\theta - \frac{1}{\theta}\right)\), we will use the chain rule and the quotient rule for differentiation.

### Step-by-step Solution:

1. **Differentiate \(x\) with respect to \(\theta\)**:
\[ x = e^{\theta} \left(\theta + \frac{1}{\theta}\right) \]
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