Find  in the following :x3 + x2 y + x y2 + y3 = 81 from M
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    Continuity and Differentiability

    Multiple Choice QuestionsShort Answer Type

    211. Differentiate x2 e3x w.r.t. (log x)2.
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    212. Differentiate space log space straight x space straight w. straight r. straight t space 1 over straight x
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    213. Differentiate space straight x squared space straight w. straight r. straight t space straight x cubed
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    214. Differentiate log (x ex) w.r.t. x log x.
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    215. Find space dy over dx space if space straight x to the power of 6 plus straight y to the power of 6 plus 6 straight x squared straight y squared equals 16.
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    216. Find dy over dx in the following :
    x2 + x y + y2 = 100 
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    217. Find dy over dx in the following :
    x3 + x2 y + x y2 + y3 = 81

    Here space straight x cubed space plus space straight x to the power of 2 space end exponent straight y space plus space straight x space straight y squared space plus space straight y to the power of 3 space end exponent equals space 81 Differntiating space both space sides space straight w. straight r. straight t space straight x comma space we space get comma space space space space space space space space straight d over dx left parenthesis straight x cubed right parenthesis plus straight d over dx left parenthesis straight x squared straight y right parenthesis plus straight d over dx left parenthesis xy squared right parenthesis plus straight d over dx left parenthesis straight y cubed right parenthesis equals straight d over dx left parenthesis 81 right parenthesis therefore space space space space 3 straight x squared plus straight x squared dy over dx plus straight y.2. straight x plus straight x.2 straight y dy over dx plus straight y squared.1 plus 3 straight y squared dy over dx equals 0 therefore space space space space left parenthesis straight x squared plus 2 xy plus 3 straight y squared right parenthesis dy over dx equals negative left parenthesis 3 straight x squared plus 2 xy plus straight y squared right parenthesis therefore space space space space space space space space space space space space space dy over dx equals negative open parentheses fraction numerator 3 straight x squared plus 2 xy plus straight y squared over denominator straight x squared plus 2 xy plus 3 straight y squared end fraction close parentheses.
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    218. Find space dy over dx space where space straight x squared over straight a squared plus straight y squared over straight b squared equals 2003
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    219. Find space dy over dx space where space 4 straight x squared plus 5 xy plus 7 straight y squared minus 8 straight x plus 9 straight y plus 3 equals 0.
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    220. Find space dy over straight d space where space straight x squared plus straight y squared equals 30 straight x space straight y
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