Question

Differentiate the following w.r.t.x: $cos to the power of negative 1 end exponent left parenthesis 4 straight x cubed minus 3 straight x right parenthesis comma space 1 half less than straight x less than 1$

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Solution

Let space space straight y equals cos to the power of negative 1 end exponent left parenthesis 4 straight x cubed minus 3 straight x right parenthesis 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 4 cos cubed space straight theta minus 3 cos space straight theta right parenthesis equals cos to the power of negative 1 end exponent left parenthesis cos space 3 straight theta right parenthesis equals 3 straight theta therefore space space space space straight y equals 3 cos to the power of negative 1 end exponent straight x space rightwards double arrow space dy over dx equals negative fraction numerator 3 over denominator square root of 1 minus straight x squared end root end fraction

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