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Continuity And Differentiability

Question

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Use Chain Rule to differentiate w.r.t.x: tan (2 x + 3)

Solution

Let space space space space space straight y equals tan left parenthesis 2 straight x plus 3 right parenthesis equals tan space straight u space where space straight u equals 2 straight x plus 3 therefore space dy over dx equals sec squared straight u comma space du over dx equals 2 By space Chain space Rule comma space space space space space dy over dx equals dy over dx du over dx equals left parenthesis sec squared straight u right parenthesis left parenthesis 2 right parenthesis equals 2 sec squared straight u therefore space dy over dx equals 2 sec squared left parenthesis 2 straight x plus 3 right parenthesis

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