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Continuity And Differentiability

Question

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$Find space fraction numerator straight d squared straight y over denominator dx squared end fraction comma space if space space straight y equals straight x cubed plus tan space straight x$

Solution

space space space space space space space space space space space straight y equals straight x cubed plus tan space straight x therefore space space dy over dx equals 3 space straight x squared plus sec squared space straight x equals 3 space straight x squared plus 1 plus tan squared space straight x therefore space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 6 space straight x plus 0 plus 2 space tan space straight x. sec squared straight x therefore space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 6 space straight x plus 2 space tan space straight x space sec squared space straight x

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