Question

$Differentiate space the space following space straight w. straight r. straight t. straight x colon cos to the power of negative 1 end exponent straight x left parenthesis 2 straight x squared minus 1 right parenthesis comma space straight x greater than 0$

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Solution

Let space space straight y equals cos to the power of negative 1 end exponent straight x left parenthesis 2 straight x squared minus 1 right parenthesis space semicolon space Put space straight x equals cos space straight theta therefore space space space space straight y equals cos to the power of negative 1 end exponent left parenthesis 2 cos squared space straight theta minus 1 right parenthesis equals cos to the power of negative 1 end exponent left parenthesis cos space 2 straight theta right parenthesis equals 2 straight theta therefore space space space space straight y equals cos to the power of negative 1 end exponent straight x space space rightwards double arrow space dy over dx equals negative fraction numerator 2 over denominator square root of 1 minus straight x squared end root end fraction

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