Question

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

Answer 1

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

Explanation:

`x=t-lnt`
`dx/dt=1-1/t`

Also,

`y=te^t`
`dy/dt=e^t+te^t=e^t(1+t)`

(Used product rule.)

`f'(t)=dy/dx=(dy/dt)/(dx/dt)=(e^t(1+t))/(1-1/t)=(te^t(1+t))/(t-1)`