Question

How do you differentiate the following parametric equation: `x(t)=e^t-cost-t, y(t)=e^t-tsint`?

Answer 1

Derivative is `(e^t-sint-tcost)/(e^t+sint-1)`

Explanation:

The differential of a parametric equation of the type `f(x(t),y(t))` is given by `((dy)/(dt))/((dx)/(dt))`.

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

and as `y(t)=e^t-tsint`, `(dy)/(dt)=e^t-sint-tcost`

Hence `(df)/(dx)=(e^t-sint-tcost)/(e^t+sint-1)`