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Continuity And Differentiability

Question

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Use Chain Rule to differentiate sin (x²) w.r.t.x.

Solution

Let space space space space space straight y equals sin left parenthesis straight x squared right parenthesis equals sin space straight u space where space straight u equals straight x squared therefore space dy over dx equals cos space straight u comma space du over dx equals 2 straight x By space Chain space Rule comma space space space space space dy over dx equals dy over du du over dx equals left parenthesis cos space straight u right parenthesis left parenthesis 2 straight x right parenthesis equals 2 straight x space cos space straight u therefore space dy over dx equals 2 straight x space cos left parenthesis straight x squared right parenthesis

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