Proof by Contradiction Using Rolle's Theorem - Calculus 1 Example

Proving a function cannot have 2 real roots using Rolle's Theorem and proof by contradiction. Disclaimer: I have an engineering degree, not a math degree. Math majors feel free to nit pick the rigour of this proof!

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Why is it -x(-sin(x)) at 4:01, not -xsin(x)?

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