Answer
$2$
Work Step by Step
Given: $x=lnt$ and $y=1+t^{2}$
$\frac{dx}{dt}=\frac{1}{t}$
$\frac{dy}{dt}=2t$
$\frac{dy}{dx}=\frac{{dy}/{dt}}{{dx}/{dt}}=\frac{2t}{1/t}=2t^{2}$
Let $m$ be the slope of the tangent line to the given curve.
$m=\frac{dy}{dx}|_{t=1}=2t^{2}|_{t=1}$
$=2\times(1)^{2}$
Hence, $m=2$
