diferentiate wrt x

If y = sin { 2 tan-1 ( 1 – x / 1 + x)1/2} show that dy / dx = -x / (1- x2)1/2

Asked by haroonrashidgkp | 27th May, 2018, 12:54: PM

Expert Answer:

begin mathsize 16px style straight y equals sin open parentheses 2 tan to the power of negative 1 end exponent open parentheses square root of fraction numerator 1 minus straight x over denominator 1 plus straight x end fraction end root close parentheses close parentheses
straight x space equals cosθ space rightwards double arrow space straight theta equals cos to the power of negative 1 end exponent straight x
straight y equals sin open parentheses 2 tan to the power of negative 1 end exponent open parentheses square root of fraction numerator 1 minus cosθ over denominator 1 plus cosθ end fraction end root close parentheses close parentheses
straight y equals sin open parentheses 2 tan to the power of negative 1 end exponent open parentheses square root of fraction numerator 2 sin squared begin display style bevelled straight theta over 2 end style over denominator 2 cos squared bevelled straight theta over 2 end fraction end root close parentheses close parentheses
straight y equals sin open parentheses 2 tan to the power of negative 1 end exponent open parentheses tan straight theta over 2 close parentheses close parentheses
straight y equals sinθ
dy over dθ equals cosθ
dy over dx equals dy over dθ cross times dθ over dx
dy over dx equals cosθ cross times fraction numerator straight d cos to the power of negative 1 end exponent straight x over denominator dx end fraction
dy over dx equals cosθ cross times fraction numerator negative 1 over denominator square root of 1 minus straight x squared end root end fraction
end style

Answered by Sneha shidid | 28th May, 2018, 10:48: AM