Question

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

Answer 1

Given $x=t+\frac{1}{t},y=t-\frac{1}{t}$

now differentiating x w.r.t 't' we get

$\frac{dx}{dt}=1-\frac{1}{t^2}$ ________ (1)

Now differentiating y wrt 't' we get

$\frac{dy}{dt}=1+\frac{1}{t^2}$ ________ (2)

dividing equation (2) by (1) we get

$\frac{dy}{dx}=\frac{1+\frac{1}{t^2}}{1-\frac{1}{t^2}}=\frac{t^2+1}{t^2-1}$

$[\frac{dy}{dx}=\frac{t^2+1}{t^2-1}]$