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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Critical Thinking

  • question_answer
    If \[x{{e}^{xy}}=y+{{\sin }^{2}}x\], then at \[x=0,\frac{dy}{dx}=\]  [IIT 1996]

    A) -1

    B) -2

    C) 1

    D) 2

    Correct Answer: C

    Solution :

    • We are given that \[x{{e}^{xy}}=y+{{\sin }^{2}}x\]           
    • When \[x=0\], we get \[y=0\]           
    • Differentiating both sides with respect to x, we get           
    • \[{{e}^{xy}}+x{{e}^{xy}}\left[ x\frac{dy}{dx}+y \right]=\frac{dy}{dx}+2\sin x\cos x\]                   
    • Putting \[x=0,\,y=0\], we get \[\frac{dy}{dx}=1\].


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