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CBSE Class 12-science Answered

  if y = (sinx)x + sin-1 (x)1/2, find dy/dx explain in great detail do not go shortcut
Asked by haroonrashidgkp | 13 Aug, 2018, 08:24: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight y equals open parentheses sinx close parentheses to the power of straight x plus sin to the power of negative 1 end exponent square root of straight x Let space straight u equals open parentheses sinx close parentheses to the power of straight x space and space straight v equals sin to the power of negative 1 end exponent square root of straight x straight u equals open parentheses sinx close parentheses to the power of straight x log space straight u space equals space xlog space sinx 1 over straight u du over dx equals straight x cross times 1 over sinx cross times cosx plus log space sinx du over dx equals open parentheses sinx close parentheses to the power of straight x open parentheses xcotx plus log space sinx close parentheses........... left parenthesis straight i right parenthesis straight v equals sin to the power of negative 1 end exponent square root of straight x dv over dx equals fraction numerator 1 over denominator square root of 1 minus straight x end root end fraction cross times fraction numerator 1 over denominator 2 square root of straight x end fraction.......... left parenthesis ii right parenthesis dy over dx equals du over dx plus dv over dx dy over dx equals open parentheses sinx close parentheses to the power of straight x open parentheses xcotx plus log space sinx close parentheses plus fraction numerator 1 over denominator square root of 1 minus straight x end root end fraction cross times fraction numerator 1 over denominator 2 square root of straight x end fraction......... from space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis end style
Answered by Sneha shidid | 14 Aug, 2018, 10:36: AM

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