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Math Help - arccos of arcsin?

  1. #1
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    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!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by iMath View Post
    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
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