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$\sqrt{|xy|} = 1$

Attempting to find the derivative gives me $$\frac12(xy)^{-1/2}\left(x\frac{dy}{dx} + y\right) = 0$$

But I haven't figured out how to simplify this further. My teacher says that that's all I'll need to know, but I want to understand how the derivative of $\sqrt {xy} = 1$ is $-\frac{y}x$.

Edited to explain that I know the whole thing equals zero, but how do I solve for (dy/dx)?

Attempts to solve get me this far: enter image description here

  • 1
    The expression you found should be set equal to $0$ because you differentiated *both* sides of the equation $\sqrt{xy} = 1$ with respect to $x$. If you have a product of factors equal to $0$, what can you conclude?2012-10-19
  • 0
    How is $\sqrt{|z|}=1$ different from $|z|=1$?2012-10-19
  • 1
    Your subject has $\sqrt{xy}$ while the body of the question has $\sqrt{|xy|}$. Which do you mean?2012-10-19

3 Answers 3