Question

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

Answer 1

Derivative is `-(2t+e^t)/(3t^2-3e^(3t-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-e^(3t-1)` and hence

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

and as `y(t)=-t^2-e^t`, `(dy)/(dt)=-2t-e^t`

Hence derivative is `(-2t-e^t)/(3t^2-3e^(3t-1))=-(2t+e^t)/(3t^2-3e^(3t-1))`