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CBSE Class 12-science Answered

 If y = xcot x + 2x2 – 3/x2 + x + 2, find dy/dx Mention each and every step
Asked by haroonrashidgkp | 19 Jun, 2018, 10:57: PM
answered-by-expert Expert Answer
y = xcot x + (2x2 – 3)/(x2 + x + 2)
begin mathsize 16px style straight y equals straight x to the power of cotx plus fraction numerator 2 straight x squared minus 3 over denominator straight x squared plus straight x plus 2 end fraction straight y equals straight u plus straight v straight u equals straight x to the power of cotx space space space and space straight v equals fraction numerator 2 straight x squared minus 3 over denominator straight x squared plus straight x plus 2 end fraction logu equals cotxlogx 1 over straight u du over dx equals cotx cross times 1 over straight x plus logx cross times open parentheses negative cosec squared straight x close parentheses du over dx equals straight x to the power of cotx space open parentheses cotx cross times 1 over straight x minus logx cross times cosec squared straight x close parentheses straight v equals fraction numerator 2 straight x squared minus 3 over denominator straight x squared plus straight x plus 2 end fraction dv over dx equals fraction numerator open parentheses straight x squared plus straight x plus 2 close parentheses cross times 4 straight x minus open parentheses 2 straight x squared minus 3 close parentheses open parentheses 2 straight x plus 1 close parentheses over denominator open parentheses straight x squared plus straight x plus 2 close parentheses squared end fraction dv over dx equals fraction numerator 4 straight x cubed plus 4 straight x squared plus 8 straight x minus open parentheses 4 straight x cubed plus 2 straight x squared minus 6 straight x minus 3 close parentheses over denominator open parentheses straight x squared plus straight x plus 2 close parentheses squared end fraction dv over dx equals fraction numerator 4 straight x squared minus 2 straight x squared plus 8 straight x plus 6 straight x plus 3 over denominator open parentheses straight x squared plus straight x plus 2 close parentheses squared end fraction dv over dx equals fraction numerator 2 straight x squared plus 14 straight x plus 3 over denominator open parentheses straight x squared plus straight x plus 2 close parentheses squared end fraction dy over dx equals straight x to the power of cotx space open parentheses cotx cross times 1 over straight x minus logx cross times cosec squared straight x close parentheses plus fraction numerator 2 straight x squared plus 14 straight x plus 3 over denominator open parentheses straight x squared plus straight x plus 2 close parentheses squared end fraction end style
Answered by Sneha shidid | 20 Jun, 2018, 10:02: AM

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