find the derivative for f(x)= sin^2x/1+cos2x?

Question

top divided by the bottom ( qoutient rule)

Answer 1

How are you going to learn having others do your homework for you? Sounds like back to the book for you!

Answer 2

The quotient rule essentially says bottom times the derivative of the top minus the top times the derivative of the bottom, all over the bottom squared.

Your function is not entirely clear. I'm assuming you mean
(sinx)^2 / (1 + cos(2x))
If this is the case, the derivative of the top is 2sinxcosx, and the derivative of the bottom is -2sin(2x).

You'd have [(1 + cos2x)(2sinxcosx) - ((sinx)^2(-2sin(2x))] / (1+cos(2x))^2.

While technically that would be a correct answer, it's almost certainly not the "back of the book" answer. You'd most likely use a variety of trig identities, particularly the double angle identities, since "2x" comes up in these expressions, to simplify things down.