Find $\frac{d(y^2)}{d(x^2)}$: Understand This Token

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SUMMARY

The discussion centers on the differentiation of the expression \(\frac{d(y^2)}{d(x^2)}\) where \(y = x^2 + 3x\). Participants clarify that the notation is unconventional and suggest interpreting it as \(\frac{(dy)^2}{(dx)^2}\), which equals \((\frac{dy}{dx})^2\). The approach involves substituting \(u = x^2\) and \(v = y^2\) to compute \(\frac{dv}{du}\) before reverting to the original variables. This method provides a clear pathway to understanding the differentiation process in this context.

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MHD93
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Let y = x^2 + 3x

and the question is Find [itex]\frac{dy^2}{dx^2}[/itex]

then how do I understand this token? is it [itex]\frac{d(y^2)}{d(x^2)}[/itex]
or [itex]\frac{(dy)^2}{(dx)^2}[/itex] = [itex](\frac{dy}{dx})^2[/itex]
or what ?

BTW: it's not wrong written, namely, not [itex]\frac{d^2y}{dx^2}[/itex]
 
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The notation is unusual. I would guess that you let u=x2 and v=y2, and compute dv/du. Then put x and y back into the result.
 
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