This is a noob calculus question.
(1) $\sqrt{|xy|} = \sqrt[4]{x^2y^2}$, are the 2 expressions equal?
if yes to (1),
then why $\frac{d}{dx}\sqrt{|xy|} \neq \frac{d}{dx}\sqrt[4]{x^2y^2}$ ?
as $\frac{d}{dx}\sqrt{|xy|} =\frac{\sqrt[4]{x^2y^2}}{2x} $
but $\frac{d}{dx}\sqrt[4]{x^2y^2} = \frac{0.5xy^2}{(x^2y^2)^{0.75}}$
i obtained the above derivatives from wolfram alpha.
-updated- yup, i think they are just 2 different way of presentation, seems like they have the same graph, thanks for the clarification.