Question

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `sinx/(1 + cosx)`

Answer 1

y = `sinx/(1 + cosx)`

= `u/v`  ....(say)

u = sin x  v = 1 + cos x

u’ = cos x v’ = – sin x

y = `u/v`

⇒ y' = `(vu"'" - uv"'")/v^2`

(i.e.,) `("d"y)/("d"x) = ((1 + cosx) cosx - sin(0 - sinx))/(1 + cosx)^2`

`("d"y)/("d"x) = (cosx + cos^2 x - sin^2x)/(1 + cosx)^2`

`("d"y)/("d"x) = (1 + cos x)/(1 + cosx)^2`

= `1/(1 + cosx)`