How do you differentiate y=(sinx/(1+cosx))^2?

1 Answer
Noah G
May 5, 2017

This can be simplified to

y = sin^2x/(1 + cosx)^2

y = (1 - cos^2x)/(1 + cosx)^2

y = ((1 + cosx)(1 - cosx))/(1 + cosx)^2

y = (1 - cosx)/(1 + cosx)

Now use the quotient rule.

y' = (sinx(1 + cosx) - (1 - cosx)-sinx)/(1 + cosx)^2

y' = (sinx + sinxcosx - (-sinx + sinxcosx))/(1 + cosx)^2

y' = (sinx + sinxcosx + sinx - sinxcosx)/(1 + cosx)^2

y' = (2sinx)/(1 + cosx)^2

Hopefully this helps!

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