Question

What is the derivative of `f(t) = (t-lnt, t^2sint )`?

Answer 1

`f'(t)=(y'(t))/(x'(t))`

`x'(t)=1-1/t = (t-1)/t`

`y'(t) = 2tsint+t^2cost`

`f'(t) = (2tsint+t^2cost)/((t-1)/t)`

`f'(t) = (t^2(2sint+tcost))/(t-1)`