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Determine dy/dx of the following and simplify if possible

  1. Aug 12, 2015 #1
    y=##sin^{-1}(\frac{x-1}{x+1})##

    My attempt:

    ##\frac{dy}{dx}## = ##\frac{1}{\sqrt{1-(\frac{(x-1)}{(x+1)})^2}}## . ##\frac{d}{dx}(\frac{x-1}{x+1})##

    = ##\frac{1}{\sqrt{(\frac{(x+1)^2-(x-1)^2}{(x+1)^2}}}## . ##\frac{(x+1)(1)-(x-1)(1)}{(x+1)^2}##

    = ##\frac{x+1}{\sqrt{x^2+2x+1-x^2+2x-1}}## . ##\frac{(x+1-x+1)}{(x+1)^2}##

    = ##\frac{x+1-x+1}{(x+1)(\sqrt4x)}##

    = ##\frac{2}{(x+1)(\sqrt4x)}##
     
  2. jcsd
  3. Aug 12, 2015 #2

    PeroK

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    It's correct except for a typo in your latex. It should be ##\sqrt{4x}##

    It's better to post in the homework section.
     
  4. Aug 16, 2015 #3
    Final answer attached. Thanks to all who helped.
     

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