Homework Help

Find `dy/dx` given that `x=3/t` and  `y=sqrt(t)*e^(-t)`

user profile pic

dawks | Student, Undergraduate | Honors

Posted September 25, 2012 at 1:29 AM via web

dislike 1 like

Find `dy/dx` given that `x=3/t` and  `y=sqrt(t)*e^(-t)`

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 25, 2012 at 2:27 AM (Answer #1)

dislike 1 like

The expression in terms of t for x is `x = 3/t` and for y it is `y = e^(-t)*sqrt t`

 `dy/dt = -e^(-t)*sqrt t + e^(-t)*(1/(2*sqrt t))`

 `dx/dt = -3/t^2`

 `dy/dx = (dy/dt)/(dx/dt)` = `(-e^(-t)*sqrt t + e^(-t)*(1/(2*sqrt t)))/(-3/t^2)` ` `

= `(t^2*e^(-t)(2*t - 1))/(6*sqrt t)`

= `(t^2*e^(-t)(2*t - 1))/(6*sqrt t)`` `

The derivative `dy/dx = (t^2*e^(-t)(2*t - 1))/(6*sqrt t)`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes