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Continuity And Differentiability

Question

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Differentiate w.r.t.x: $space straight y equals sin left parenthesis ax plus straight b right parenthesis$

Solution

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight y equals sin left parenthesis ax plus straight b right parenthesis therefore space space space space space space space space space space space space space space space space space space space space space dy over dx equals straight d over dx left square bracket sin left parenthesis ax plus straight b right parenthesis right square bracket equals cos left parenthesis ax plus straight b right parenthesis. straight d over dx left parenthesis ax plus straight b right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals cos left parenthesis ax plus straight b right parenthesis. straight a therefore space straight d over dx left square bracket sin left parenthesis ax plus straight b right parenthesis right square bracket equals straight a space cos left parenthesis ax plus straight b right parenthesis

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