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Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
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Solution
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)`
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