Question

How do you differentiate `s=(1+sint)/(1+cost)`?

Answer 1

`(ds)/(dt) = ( 1+ cost + sint)/(1+cost)^2`

Explanation:

Using the quotient rule:

`(ds)/(dt) = ( (1+cost) d/(dt) (1+sint) - (1+sint) d/(dt) (1+cost))/(1+cost)^2`

`(ds)/(dt) = ( (1+cost) cost + (1+sint) sint)/(1+cost)^2`

`(ds)/(dt) = ( cost+cos^2t + sint+sin^2t)/(1+cost)^2`

`(ds)/(dt) = ( 1+ cost + sint)/(1+cost)^2`