Question

How do you differentiate the following parametric equation: `x(t)=t-(t+1)e^t, y(t)= t^2-e^(t-1)`?

Answer 1

Solution: `x'(t)=1-te^t-2e^t` , `y'(t)=2t-e^(t-1)`

Explanation:

`x'(t)=(t)'-(t+1)'e^t-(t+1)(e^t)'` =
`1-e^t-(t+1)e^t` `=1-e^t-te^t-e^t= 1-te^t-2e^t`

`y'(t)=2t-e^(t-1)(t-1)'` =
`2t-e^(t-1)`