Question

What is the derivative of `f(t) = (t^2-sint , 1/(t^2-1) )`?

Answer 1

Derivative of `f(t)` is `-(2t)/((2t-cost)(t^2-1)^2)`

Explanation:

The derivative of a function `f(t)=(x(t),y(t))` is given by `((dy)/(dt))/((dx)/(dt))`

as `x(t)=t^2-sint` we have `(dx)/(dt)=2t-cost` and

for `y(t)=1/(t^2-1)` we have `(dy)/(dt)=-(2t)/(t^2-1)^2`

Hence derivative of `f(t)=(t^2-sint,1/(t^2-1))`

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