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CBSE Class 12-science Answered

if y = sin^-1 [ {5x + 12(1-x^2)^1/2} / 13 ] find dy/dx
Asked by Jerrin Thomas | 11 Feb, 2015, 03:21: PM
answered-by-expert Expert Answer
G i v e n space y equals sin to the power of negative 1 end exponent fraction numerator 5 x plus 12 square root of 1 minus x squared end root over denominator 13 end fraction I f space y equals sin to the power of negative 1 end exponent x comma space t h e n space fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction T h u s comma fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator square root of 1 minus open square brackets fraction numerator 5 x plus 12 square root of 1 minus x squared end root over denominator 13 end fraction close square brackets squared end root end fraction cross times fraction numerator d over denominator d x end fraction open square brackets fraction numerator 5 x plus 12 square root of 1 minus x squared end root over denominator 13 end fraction close square brackets space space space space space space equals fraction numerator 1 over denominator square root of 1 minus open square brackets fraction numerator 5 x plus 12 square root of 1 minus x squared end root over denominator 13 end fraction close square brackets squared end root end fraction cross times open square brackets fraction numerator 5 minus begin display style fraction numerator 12 over denominator square root of 1 minus x squared end root end fraction end style over denominator 13 end fraction close square brackets space space space space space space equals fraction numerator 5 minus fraction numerator 12 over denominator square root of 1 minus x squared end root end fraction over denominator 13 begin display style fraction numerator square root of 169 minus 25 x squared minus 144 open parentheses 1 minus x squared close parentheses minus 120 square root of 1 minus x squared end root end root over denominator 13 end fraction end style end fraction space space space space space space equals fraction numerator 5 minus fraction numerator 12 over denominator square root of 1 minus x squared end root end fraction over denominator begin display style square root of 169 minus 25 x squared minus 144 open parentheses 1 minus x squared close parentheses minus 120 square root of 1 minus x squared end root end root end style end fraction space space space space space space equals fraction numerator 5 minus fraction numerator 12 over denominator square root of 1 minus x squared end root end fraction over denominator begin display style square root of 119 x squared minus 120 square root of 1 minus x squared end root plus 25 end root end style end fraction
Answered by Vimala Ramamurthy | 12 Feb, 2015, 11:48: AM
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