Determine dy/dx of the following and simplify if possible

  • Thread starter DevonZA
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  • #1
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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)}##
 

Answers and Replies

  • #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.
 
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  • #3
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Final answer attached. Thanks to all who helped.
 

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