Solve this question?i f space y equals x over 2 square root of left parenthesis a squared end root minus x squared right parenthesis plus a squared over 2 sin to the power of negative 1 end exponent left parenthesis x over a right parenthesis space t h e n space p r o v e space t h a t space fraction numerator d y over denominator d x end fraction equals square root of left parenthesis a squared end root minus x squared right parenthesis.

Asked by 2330anurag | 26th Jul, 2015, 07:32: PM

Expert Answer:

y equals x over 2 square root of a squared minus x squared end root plus a squared over 2 s i n to the power of negative 1 end exponent x over a D i f f e r e n t i a t i n g space w i t h space r e s p e c t space t o space apostrophe x apostrophe comma space w e space g e t rightwards double arrow fraction numerator d y over denominator d x end fraction equals x over 2 fraction numerator negative 2 x over denominator 2 square root of a squared minus x squared end root end fraction plus fraction numerator square root of a squared minus x squared end root over denominator 2 end fraction plus a squared over 2 cross times 1 over a fraction numerator 1 over denominator square root of 1 minus open parentheses begin display style x over a end style close parentheses squared end root end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator negative x squared over denominator 2 square root of a squared minus x squared end root end fraction plus fraction numerator square root of a squared minus x squared end root over denominator 2 end fraction plus a squared over 2 fraction numerator 1 over denominator square root of a squared minus x squared end root end fraction  rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator a squared minus x squared over denominator 2 square root of a squared minus x squared end root end fraction plus fraction numerator square root of a squared minus x squared end root over denominator 2 end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator square root of a squared minus x squared end root over denominator 2 end fraction plus fraction numerator square root of a squared minus x squared end root over denominator 2 end fraction equals square root of a squared minus x squared end root

Answered by satyajit samal | 27th Jul, 2015, 10:10: AM