Find fraction numerator d y over denominator d x end fraction space i f space y equals fraction numerator 3 minus u over denominator 2 plus u end fraction comma u equals fraction numerator 4 x over denominator 1 minus x squared end fraction

Asked by sunil2791 | 23rd May, 2017, 12:20: PM

Expert Answer:

begin mathsize 16px style straight y equals fraction numerator 3 minus straight u over denominator 2 plus straight u end fraction
dy over du equals fraction numerator open parentheses 2 plus straight u close parentheses begin display style fraction numerator straight d open parentheses 3 minus straight u close parentheses over denominator du end fraction end style minus open parentheses 3 minus straight u close parentheses begin display style fraction numerator straight d open parentheses 2 plus straight u close parentheses over denominator du end fraction end style over denominator open parentheses 2 plus straight u close parentheses squared end fraction
dy over du equals fraction numerator negative open parentheses 2 plus straight u close parentheses minus open parentheses 3 minus straight u close parentheses over denominator open parentheses 2 plus straight u close parentheses squared end fraction
dy over du equals fraction numerator negative 2 minus straight u minus 3 plus straight u over denominator open parentheses 2 plus straight u close parentheses squared end fraction
dy over du equals fraction numerator negative 6 over denominator open parentheses 2 plus straight u close parentheses squared end fraction
and space
straight u equals fraction numerator 4 straight x over denominator 1 minus straight x squared end fraction
du over dx equals fraction numerator open parentheses 1 minus straight x squared close parentheses 4 minus 4 straight x open parentheses negative 2 straight x close parentheses over denominator open parentheses 1 minus straight x squared close parentheses squared end fraction
du over dx equals fraction numerator 4 minus 4 straight x squared plus 8 straight x squared over denominator open parentheses 1 minus straight x squared close parentheses squared end fraction
rightwards double arrow dy over dx equals dy over du cross times du over dx space using space chain space rule.
rightwards double arrow dy over dx equals fraction numerator negative 6 over denominator open parentheses 2 plus straight u close parentheses squared end fraction cross times fraction numerator 4 minus 4 straight x squared plus 8 straight x squared over denominator open parentheses 1 minus straight x squared close parentheses squared end fraction
where space straight u equals fraction numerator 4 straight x over denominator 1 minus straight x squared end fraction

end style

Answered by Sneha shidid | 23rd May, 2017, 05:09: PM

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