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CBSE Class 12-science Answered

1. Differentiate Sec-1 (1/2x2 – 1) with respect to root 1 – x2 . 2. If y = x4e2x, then find yn .
Asked by arnavmohanty1999 | 13 Apr, 2017, 05:24: PM
answered-by-expert Expert Answer

begin mathsize 16px style Let comma space Sec to the power of negative 1 end exponent space open parentheses fraction numerator 1 over denominator 2 straight x to the power of 2 space end exponent – space 1 end fraction close parentheses space equals straight u straight u equals cos to the power of negative 1 end exponent open parentheses 2 straight x to the power of 2 space end exponent – space 1 close parentheses straight x equals cosθ straight u equals cos to the power of negative 1 end exponent open parentheses 2 cos to the power of 2 space end exponent straight theta – space 1 close parentheses straight u equals cos to the power of negative 1 end exponent open parentheses cos 2 straight theta close parentheses straight u equals 2 straight theta but space straight theta equals cos to the power of negative 1 end exponent straight x du over dx equals fraction numerator negative 1 over denominator square root of 1 minus straight x squared end root end fraction let space straight v equals square root of 1 minus straight x squared end root dv over dx equals fraction numerator 1 over denominator 2 square root of 1 minus straight x squared end root end fraction cross times negative 2 straight x equals fraction numerator negative straight x over denominator square root of 1 minus straight x squared end root end fraction using space fraction numerator du divided by dx over denominator dv divided by dx end fraction equals fraction numerator fraction numerator negative 1 over denominator square root of 1 minus straight x squared end root end fraction over denominator fraction numerator negative straight x over denominator square root of 1 minus straight x squared end root end fraction end fraction equals 1 over straight x end style

Answered by | 13 Apr, 2017, 06:02: PM

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