## Whatever1 Group Title what is y' in Arc csc squaroot of 2x one year ago one year ago

1. satellite73

$y=\csc^{-1}(\sqrt{2x})$?

2. satellite73

if i recall correctly the derivative of $$\csc^{-1}(x)$$ is $$-\frac{1}{x\sqrt{x^2-1}}$$

3. satellite73

yeah i got it

4. Whatever1

the y'

5. satellite73

so you want $$\frac{d}{dx}[\csc^{-1}(\sqrt{2x})]$$

6. satellite73

what you need is the derivative of $$\csc^{-1}(x)$$ and the chain rule

7. satellite73

$\frac{d}{dx}[\csc^{-1}(x)=-\frac{1}{x\sqrt{x^2-1}}$ 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