# How do you differentiate the following parametric equation:  x(t)=tlnt, y(t)= cost-sin^2t ?

Parametric differentiation: if $x = x \left(t\right)$ and $y = y \left(t\right)$ then
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}$
provided that $\frac{\mathrm{dx}}{\mathrm{dt}}$ is not zero.
dy/dx=[-sint-2sintcost]/[lnt+t*1/t]=> dy/dx=[-sint*(1+2cost)]/[1+lnt]