Practise reciprocal and trigonometric derivative ratios

$dy/dt=1/t^2$, $dx/dt=4$, so $dy/dx=1/(4t^2)$, $t\ne0$.

$dy/dt=3\cos t$, $dx/dt=-4\sin t$, so $dy/dx=-3\cos t/(4\sin t)=-\tfrac34\cot t$, wherever $\sin t\ne0$. At the remaining ellipse endpoints use vertical-tangent analysis rather than dividing by zero.