Archive
13th of April 2017
Mathematics
Q:


1. Differentiate Sec-1 (1/2x2 – 1) with respect to root 1 – x2 .


2. If y = x4e2x, then find yn .


Arnav Mohanty - CBSE - Class XII Science

Thursday, April 13, 2017 at 17:24:PM

A:

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

Thursday, April 13, 2017 at 18:02:PM