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Could you explain it to me please?

Are you familiar with the derivative rules?

Yes

How does the product rule look like when you derive \(\ x^2y?\)

It should be f'(x) *y + f(x) *y'. Derivative of x^2 is 2x and derivative of y is dy/dx.

Could you show me the product rule in terms of \(\ x^2y \text{, please?}\)

Sure (2x)(y) +(x^2)(dy/dx)

What does the dy/dx mean? dy/dx of x^2? or y?

I'm REALLY Confused BY this! !

it's the derivative of y

Let's say you had y^3 you would derive it as \[3y^2 \frac{ dy }{ dx }\]

Okay