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

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sciencesolve eNotes educator| Certified Educator

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).`

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