Question

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

Answer 1

`(df)/(dx)=(1-e^t)/(2t-cost)`

Explanation:

Derivative of `f(t)=(x(t),y(t))` is given by `(df)/(dx)=((dy)/(dt))/((dx)/(dt))`

As `x(t)=t^2-sint`, `(dx)/(dt)=2t-cost`

and `y(t)=t-e^t`, `(dy)/(dt)=1-e^t`

Hence `(df)/(dx)=(1-e^t)/(2t-cost)`