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JEE Main & Advanced Mathematics Differentiation Question Bank Partial Differentiation

  • question_answer
    If \[u=x{{y}^{2}}{{\tan }^{-1}}\left( \frac{y}{x} \right)\], then \[x{{u}_{x}}+y{{u}_{y}}=\]                 [EAMCET 2001]

    A)            2u

    B)            u

    C)            3u

    D)            u/3

    Correct Answer: C

    Solution :

               \[u={{x}^{3}}{{\left( \frac{y}{x} \right)}^{2}}{{\tan }^{-1}}\left( \frac{y}{x} \right)\] is homogeneous in x, y of degree 3. \[\therefore \] \[x{{u}_{x}}+y{{u}_{y}}=3u\].


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