What did everyone get for the question that was:
"Given x = ln(sec(2y)), work out dy/dx as a function of x"
I got 1/(2(e^x)sin(arccos(1/(e^x))))
Since dx/dy is 2tan(2y), we know that dy/dx = 1/(dx/dy) = 1/2 * cot(2y). We also can rearrange x to get y=
x = ln(sec(2y))
e^x = sec(2y)
1/(e^x) = cos(2y)
y = arccos(1/(e^x)) / 2
Which we then sub in as
1/2 * cot(arccos(1/(e^x)))
Which gets us to
1/2 * (cos(arccos(1/(e^x))) / sin(arccos(1/(e^x)))
Which is then
1/(2(e^x)sin(arccos(1/(e^x))))
Not sure if I've oversimplified (or undersimplified), but that's what I got.