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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
     If \[y=\frac{{{(1-x)}^{2}}}{{{x}^{2}}}\], then \[\frac{dy}{dx}\]is                                          [MP PET 1999]

    A)  \[\frac{2}{{{x}^{2}}}+\frac{2}{{{x}^{3}}}\]

    B)  \[-\frac{2}{{{x}^{2}}}+\frac{2}{{{x}^{3}}}\]

    C)  \[-\frac{2}{{{x}^{2}}}-\frac{2}{{{x}^{3}}}\]

    D)   \[-\frac{2}{{{x}^{3}}}+\frac{2}{{{x}^{2}}}\]

    Correct Answer: D

    Solution :

               \[y=\frac{1+{{x}^{2}}-2x}{{{x}^{2}}}=\frac{1}{{{x}^{2}}}+1-\frac{2}{x}\Rightarrow \frac{dy}{dx}=-\frac{2}{{{x}^{3}}}+\frac{2}{{{x}^{2}}}\].


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