Homework Help

If x=ln (t+1) and  y=ln (t+2), then dy/dx=?

user profile pic

yapayapa | Honors

Posted July 4, 2013 at 5:12 PM via web

dislike 1 like

If x=ln (t+1) and  y=ln (t+2), then dy/dx=?

Tagged with calculus test, math

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 4, 2013 at 5:42 PM (Answer #1)

dislike 0 like

You need to evaluate `(dy)/(dt)` and `(dx)/(dt)` , using the chain rule, such that:

`(dy)/(dt) = (d(ln(t+2)))/(dt) => (dy)/(dt) = 1/(t+2)`

`(dx)/(dt) = (d(ln(t+1)))/(dt) => (dx)/(dt) = 1/(t+1)`

You need to evaluate `(dy)/(dx)` , such that:

`(dy)/(dx) = ((dy)/(dt))/((dx)/(dt))`

`(dy)/(dx) = (1/(t+2))/(1/(t+1))`

`(dy)/(dx) = (t+1)/(t+2)`

Hence, evaluating the derivative `(dy)/(dx)` , under the given conditions, yields `(dy)/(dx) = (t+1)/(t+2).`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes