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Continuity And Differentiability

Question

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Differentiate the following functions w.r.t.x: $cos to the power of negative 1 end exponent left parenthesis sin space straight x right parenthesis$

Solution

Let space space space space straight y equals cos to the power of negative 1 end exponent left parenthesis sin space straight x right parenthesis equals cos to the power of negative 1 end exponent open square brackets cos open parentheses straight pi over 2 minus straight x close parentheses close square brackets therefore space space space space space space straight y equals straight pi over 2 minus straight x therefore space dy over dx equals negative 1

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