Differentiate sin open square brackets 2 tan to the power of negative 1 end exponent square root of fraction numerator 1 minus x over denominator 1 plus x end fraction end root close square brackets

Asked by sunil2791 | 23rd May, 2017, 12:23: PM

Expert Answer:

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

Answered by Sneha shidid | 23rd May, 2017, 01:46: PM