Question

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

Answer 1

`(dy)/(dx)=(cost-sint)/(t+1)`

Explanation:

Derivative of a parametric equation of type `f(t)=(x(t),y(t))`

is given by `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

Here `(dy)/(dt)=e^tcost-e^tsint=e^t(cost-sint)`

and `(dx)/(dt)=te^t+e^t=e^t(t+1)`

Hence `(dy)/(dx)=(e^t(cost-sint))/(e^t(t+1))=(cost-sint)/(t+1)`