Question

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

Answer 1

Parametric differentiation: if `x = x(t)` and `y = y(t)` then

`dy/dx=[dy/dt]/[dx/dt]`

provided that `dx/dt` is not zero.

Hence

#dy/dx=[-sint-2sintcost]/[lnt+t*1/t]=> dy/dx=[-sint*(1+2cost)]/[1+lnt]#