Find `(dy)/(dx)` , when `x=e^(theta)(theta+1/theta)` and `y=e^(-theta)(theta-1/theta)`

Explanation

To find \(\frac{dy}{dx}\) given the equations for \(x\) and \(y\) in terms of \(\theta\), we will follow these steps:

1. **Differentiate \(x\) with respect to \(\theta\)**:
\[ x = e^{\theta} \left( \theta + \frac{1}{\theta} \right) \]
We will use the product rule for differentiation. The product rule states that if \(u\) and \(v\) are functions of \(\theta\), then:
\[
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