Thread: arccos of arcsin?

Question: "Find the derivative of arccos(arcsin(t))".

which should be same as cos^-1 (sin^-1 (t))

I have no idea how to approach this problem. I know that sin(arcsinx) = x if [-1,1] and arc(sinx) = x if [-pi/2, pi/2] but my prof never explained the arccos and thats why I really don't know how to start doing this question!

Originally Posted by iMath

Question: "Find the derivative of arccos(arcsin(t))".

which should be same as cos^-1 (sin^-1 (t))

I have no idea how to approach this problem. I know that sin(arcsinx) = x if [-1,1] and arc(sinx) = x if [-pi/2, pi/2] but my prof never explained the arccos and thats why I really don't know how to start doing this question!

you are not asked to evaluate the function, you are asked to find its derivative.

recall that and

now use the chain rule