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Continuity And Differentiability

Question

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Differentiate sin x²w.r.t.x².

Solution

Let space space space space space straight y equals sin space straight x squared comma space straight u equals straight x squared therefore space dy over dx equals left parenthesis cos space straight x squared right parenthesis comma space 2 straight x equals 2 straight x space cos space straight x squared space space space space space du over dx equals 2 straight x Now space dy over du equals fraction numerator begin display style dy over dx end style over denominator begin display style du over dx end style end fraction equals fraction numerator 2 straight x space cos space straight x squared over denominator 2 straight x end fraction equals cos space straight x squared

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