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Whatever1 Group Title

what is y' in Arc csc squaroot of 2x

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    \[y=\csc^{-1}(\sqrt{2x})\]?

    • one year ago
  2. satellite73 Group Title
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    if i recall correctly the derivative of \(\csc^{-1}(x)\) is \(-\frac{1}{x\sqrt{x^2-1}}\)

    • one year ago
  3. satellite73 Group Title
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    yeah i got it

    • one year ago
  4. Whatever1 Group Title
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    the y'

    • one year ago
  5. satellite73 Group Title
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    so you want \(\frac{d}{dx}[\csc^{-1}(\sqrt{2x})]\)

    • one year ago
  6. satellite73 Group Title
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    what you need is the derivative of \(\csc^{-1}(x)\) and the chain rule

    • one year ago
  7. satellite73 Group Title
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    \[\frac{d}{dx}[\csc^{-1}(x)=-\frac{1}{x\sqrt{x^2-1}}\] i know because i just looked it up replace \(x\) by \(\sqrt{2x}\) and then multiply by the derivative of \(\sqrt{2x}\) which is \(\frac{1}{\sqrt{2x}}\) then probably some algebra to clean it up

    • one year ago
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