Question

How do you differentiate the following parametric equation: `x(t)=lnt, y(t)= tcost`?

Answer 1

`dy/dx=t(cost-tsint)`

Explanation:

`x'(t)=1/t`

Product rule here:

`y'(t)=cost-tsint`

The derivative of a parametric function can be found through:

`(dy/dt)/(dx/dt)=(y'(t))/(x'(t))=(cost-tsint)/(1/t)=t(cost-tsint)`