Question

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

Answer 1

`(dy)/(dx)=(2t^2sint+t^3cost)/(t-2)`

Explanation:

Derivative `(dy)/(dx)` of `f(t)=(x(t),y(t))` is given by `((dy)/(dt))/((dx)/(dt))`

As `y(t)=t^2sint`, `(dy)/(dt)=2tsint+t^2cost`

and as `x(t)=t-lnt^2`, `(dx)/(dt)=1-(2t)/t^2=1-2/t`

Hence `((dy)/(dt))/((dx)/(dt))=(2tsint+t^2cost)/(1-2/t)`

= `(2t^2sint+t^3cost)/(t-2)`