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Continuity And Differentiability

Question

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Differentiate the following function w.r.t.x: $sin minus 1 left parenthesis cos space straight x right parenthesis comma space 0 less than straight x less than straight pi over 2$

Solution

Let space space space space space straight y equals sin minus 1 left parenthesis cos space straight x right parenthesis therefore space dy over dx equals fraction numerator 1 over denominator square root of 1 minus cos squared straight x end root end fraction. straight d over dx left parenthesis cos space straight x right parenthesis equals fraction numerator 1 over denominator sin space straight x end fraction. left parenthesis negative sin space straight x right parenthesis equals negative 1

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