Question

derivative of arcsin(cos(2x))
is this chain rule?

Answer 1

Yup. Let cos(2x) = u, then
d(arcsin(u))/du = ((1-x^2)^(-1)) * du'
Then let v = 2x, then d(cos(v)) = -sin(v) v'
It's just a double chain rule. Try it out.

Answer 2

Minor correction, I meant ^(-1/2)

Answer 3

i got -2sin(2x) * 1/(sqrt(1-(cos2x)^2)

Answer 4

Let me work this through: \[ -2\frac{1}{\sqrt{1-cos(2x)^2}} \sin(2x) \]So you are correct :-) Congrats.

Answer 5

how can I simplify the denominator?

Answer 6

double angle?

Answer 7

Hmm, I think you can do some algebra here (without double angles), but I just can't see it. Sorry, mate. :-)