Question

What is the derivative of `f(t) = (t^3-te^(1-t) , t^2-t+te^t )`?

Answer 1

`(dy)/(dx)=(2t-1+e^t(t+1))/(3t^2+e^(1-t)(t-1))`

Explanation:

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

Here `x(t)=t^3-te^(1-t)` and `y(t)=t^2-t+te^t`

therefore `(dx)/(dt)=3t^2-e^(1-t)-te^(1-t)*(-1)`

= `3t^2+e^(1-t)(t-1)`

and `(dy)/(dt)=2t-1+e^t+te^t=2t-1+e^t(t+1)`

Hence `(dy)/(dx)=(2t-1+e^t(t+1))/(3t^2+e^(1-t)(t-1))`