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Continuity And Differentiability

Question

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Differentiate w.r.t.x: $sin left parenthesis straight x squared plus 5 right parenthesis$

Solution

Let space space space space space straight y equals sin left parenthesis straight x squared plus 5 right parenthesis therefore space dy over dx equals straight d over dx left square bracket sin left parenthesis straight x squared plus 5 right parenthesis right square bracket equals cos left parenthesis straight x squared plus 5 right parenthesis. straight d over dx left parenthesis straight x squared plus 5 right parenthesis space space space space space space space space space space space space space equals cos left parenthesis straight x squared plus 5 right parenthesis. left parenthesis 2 straight x right parenthesis therefore space straight d over dx left square bracket sin left parenthesis straight x squared plus 5 right parenthesis right square bracket equals 2 straight x space cos left parenthesis straight x squared plus 5 right parenthesis

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