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Math Help - derivatives of inverse trigonometry functions

  1. #1
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    derivatives of inverse trigonometry functions

    Find the derivatives of the following:

    1) f(x) = cos-1(1/x-1)
    2) f(x) = sin-1(2x+1)
    3) f(x) = sin-1(pi/x)

    thankyou for any help given !!
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  2. #2
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    Quote Originally Posted by iiharthero View Post
    Find the derivatives of the following:

    1) f(x) = cos-1(1/x-1)
    2) f(x) = sin-1(2x+1)
    3) f(x) = sin-1(pi/x)

    thankyou for any help given !!
    In all 3 questions you have to use the chain rule. I'll show you how to do a) and leave the rest for you:

    1. f(x)=\arccos(x)~\implies~f'(x)=\dfrac{-1}{\sqrt{1-x^2}}

    f(x)=\arccos\left(\dfrac1x-1\right)~\implies~f'(x)=\dfrac{-1}{\sqrt{1-\left(\dfrac1x-1\right)^2}} \cdot \left(-\dfrac1{x^2}\right)

    2. Simplify:

    \dfrac{-1}{\sqrt{1-\dfrac1{x^2}+\dfrac2x-1}} \cdot \left(-\dfrac1{x^2}\right) =  \dfrac1{\dfrac1{|x|} \cdot \sqrt{2x-1}} \cdot \dfrac1{x^2} = \dfrac1{|x| \cdot \sqrt{2x-1}}
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