If y = (tan-1 x)2, prove that ( 1 + x2)2y2 + 2x( 1 + x2)y1 = 2

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Asked by haroonrashidgkp | 24th Aug, 2018, 10:53: PM

Expert Answer:

begin mathsize 16px style straight y equals open parentheses tan to the power of negative 1 end exponent straight x close parentheses squared
dy over dx equals 2 tan to the power of negative 1 end exponent straight x cross times fraction numerator 1 over denominator 1 plus straight x squared end fraction
open parentheses 1 plus straight x squared close parentheses dy over dx equals 2 tan to the power of negative 1 end exponent straight x
Squaring space on space both space sides comma
open parentheses 1 plus straight x squared close parentheses squared open parentheses dy over dx close parentheses squared equals 4 open parentheses tan to the power of negative 1 end exponent straight x close parentheses squared
open parentheses 1 plus straight x squared close parentheses squared open parentheses dy over dx close parentheses squared equals 4 straight y
left parenthesis 1 plus straight x squared right parenthesis squared cross times 2 dy over dx fraction numerator straight d squared straight y over denominator dx squared end fraction plus open parentheses dy over dx close parentheses squared 2 open parentheses 1 plus straight x squared close parentheses cross times 2 straight x equals 4 dy over dx
left parenthesis 1 plus straight x squared right parenthesis squared fraction numerator straight d squared straight y over denominator dx squared end fraction plus 2 straight x open parentheses dy over dx close parentheses open parentheses 1 plus straight x squared close parentheses equals 2
end style

Answered by Sneha shidid | 28th Aug, 2018, 09:30: AM