Question

What is the derivative of `f(t) = (2-te^t, 2t^2+5t )`?

Answer 1

`(dy)/(dx)=-(4t+5)/(e^t(t+1))`

Explanation:

For a parametric function `f(t)=(x(t),y(t))`

derivative `(dy)/(dx)` is defined as `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

Here `x(t)=2-te^t` hence `(dx)/(dt)=-(e^t+te^t)=-e^t(t+1)`

and as `y(t)=2t^2+5t`, `(dy)/(dt)=4t+5`

Hence `(dy)/(dx)=-(4t+5)/(e^t(t+1))`