Question

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

Answer 1

`(te^t + e^t - 2t + 1 )/ (1 + e^t)`

Explanation:

Differentiation states `dy/dx`

`x= t+ e^t`
`y= te^t-t^2+t`

Take the derivative of both functions
`x'= 1 + e^t`
`y'= d/dt (te^t) - d/dt(t^2) + d/dt (t)`
Use product rule for `te^t`, which states: f' g + f g'
`d/dt (t) * e^t + t * d/dt (e^t) - 2t + 1`

`1 * e^t + t * e^t - 2t +1`

`y'=te^t + e^t - 2t + 1`

so now `dy/dx`

`(te^t + e^t - 2t + 1 )/ (1 + e^t)`