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Continuity And Differentiability

Question

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$Find space dy over dx space when space straight x equals sin space straight t comma space straight y space equals cos space 2 straight t$

Solution

space space space space space space space space space space straight x equals sin space straight t comma space straight y space equals cos space 2 straight t therefore space dx over dt equals cos space straight t comma space dy over dt equals negative 2 space sin space 2 straight t Now space dy over dx equals fraction numerator begin display style dy over dt end style over denominator begin display style dx over dt end style end fraction equals fraction numerator negative 2 space sin space 2 straight t over denominator cos space straight t end fraction equals negative 2 fraction numerator 2 space sin space straight t space cos space straight t over denominator cos space straight t end fraction equals negative 4 space sin space straight t

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