Question

Differentiate the following functions w.r.t.x: $cos to the power of negative 1 end exponent open parentheses square root of fraction numerator 1 plus cos space straight x over denominator 2 end fraction end root close parentheses$

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Solution

Let space space space space space straight y equals cos to the power of negative 1 end exponent open parentheses square root of fraction numerator 1 plus cos space straight x over denominator 2 end fraction end root close parentheses equals cos to the power of negative 1 end exponent open parentheses square root of fraction numerator 2 cos squared begin display style straight x over 2 end style over denominator 2 end fraction end root close parentheses equals cos to the power of negative 1 end exponent open parentheses cos straight x over 2 close parentheses equals straight x over 2 therefore space dy over dx equals 1 half

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