Question

Find the second order derivatives of the following functions : tan^-1 x

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Solution

Let space space space space space space space space space straight y equals tan to the power of negative 1 end exponent space straight x space therefore space space space space space dy over dx equals fraction numerator 1 over denominator 1 plus straight x squared end fraction and space fraction numerator straight d squared straight y over denominator dx squared end fraction equals fraction numerator left parenthesis 1 plus straight x squared right parenthesis.0 minus 1.2 straight x over denominator left parenthesis 1 plus straight x squared right parenthesis squared end fraction equals negative fraction numerator 2 straight x over denominator left parenthesis 1 plus straight x squared right parenthesis squared end fraction

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