How do you find the derivative of f(x)=sin2x/cos2x

Answer 1

easy way:
sin2x/cos2x = tan2x
so the derivative is just

2sec^2(2x)

hard way, using the quotient rule:

[2cos(2x)cos(2x) - sin(2x)(-2sin(2x))]/cos^2(2x)

2(cos^2(2x)+sin^2(2x))/cos^2(2x)

2/cos^2(2x)

2sec^2(2x)