# arccos of arcsin?

• Oct 9th 2008, 11:52 PM
iMath
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!
• Oct 10th 2008, 12:51 AM
Jhevon
Quote:

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 $\frac d{dx} \arccos [f(x)] = - \frac {f'(x)}{\sqrt{1 - [f(x)]^2}}$ and $\frac d{dx} \arcsin x = \frac 1{\sqrt{1 = x^2}}$

now use the chain rule