If \(x = e^{t} + e^{-t}\) and \(y = e^{t} - e^{-t}\), \(t \ne 0\), then \(\displaystyle\frac{dy}{dx}\) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{x}{y}\)
Differentiating each with respect to t:
\( \displaystyle \frac{dx}{dt} = e^{t} - e^{-t} = y \)
\( \displaystyle \frac{dy}{dt} = e^{t} + e^{-t} = x \)
In parametric form:
\( \displaystyle \frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{x}{y} \)