Question

If $x=\theta -\frac{1}{\theta },y=\theta +\frac{1}{\theta }then\frac{dy}{dx}=$

• A. $\frac{x}{y}$
• B. $\frac{y}{x}$
• C. $\frac{-x}{y}$
• D. $\frac{-y}{x}$

Answer 1

The correct option is A $\frac{x}{y}$

Given,

$x=\theta -\frac{1}{\theta }$

$\to \frac{dx}{d\theta }=1+\frac{1}{{\theta }^2}$

$y=\theta +\frac{1}{\theta }$

$\to \frac{dy}{d\theta }=1-\frac{1}{{\theta }^2}$

$\frac{dy}{dx}=\frac{\frac{dy}{d\theta }}{\frac{dx}{d\theta }}$

$=\frac{1-\frac{1}{{\theta }^2}}{1+\frac{1}{{\theta }^2}}$

$=\frac{{\theta }^2-1}{{\theta }^2+1}=\frac{x}{y}$