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Continuity And Differentiability

Question

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Differentiate the following functions w.r.t.x: $sin space 2 straight x. cos space 3 straight x$

Solution

Here space space straight y equals sin space 2 straight x. cos space 3 straight x therefore space dy over dx equals sin 2 straight x. straight d over dx left parenthesis cos space 3 straight x right parenthesis plus cos space 3 straight x. straight d over dx left parenthesis sin space 2 straight x right parenthesis space space space space space space space space space space space space space equals sin space 2 straight x. left parenthesis negative 3 sin space 3 straight x right parenthesis plus cos space 3 straight x. left parenthesis 2 cos space 2 straight x right parenthesis space space space space space space space space space space space space space equals negative 3 sin space 2 straight x space sin space 3 straight x plus 2 cos space 2 straight x space cos 3 straight x

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