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JEE Main & Advanced Mathematics Differentiation Question Bank Partial Differentiation

  • question_answer
    If \[u={{\tan }^{-1}}\frac{y}{x}\], then by Euler?s Theorem the value of x \[\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=\]                                           [Tamilnadu (Engg.) 1993]

    A)            \[\tan u\]

    B)            \[\sin u\]

    C)            \[0\]

    D)            \[\cos 2u\]

    Correct Answer: C

    Solution :

                       \[u={{\tan }^{-1}}\frac{y}{x}={{x}^{0}}.{{\tan }^{-1}}\frac{y}{x}\]                    Clearly u is homogeneous in x, y of degree 0.                    \[\therefore \] By Euler?s theorem \[x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial z}=0.u=0\].


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