J & K CET Engineering J and K - CET Engineering Solved Paper-2014

  • question_answer Differentiate \[{{x}^{-3}}\,(2+7x)\]

    A)  \[\frac{-1}{{{x}^{4}}}\,(3+7x)\]        

    B)  \[\frac{-2}{{{x}^{3}}}\,(2+7x)\]

    C)  \[\frac{2}{{{x}^{4}}}\,(2+7x)\]

    D)  \[\frac{-2}{{{x}^{4}}}\,(3+7x)\]

    Correct Answer: D

    Solution :

    Let  \[y={{x}^{-3}}(2+7x)=2{{x}^{-3}}+7{{x}^{-2}}\] On differentiating w .r .t .x, we get \[\frac{dy}{dx}=2(-3){{x}^{-3-1}}+7(-2){{x}^{-2-1}}\] \[=-6{{x}^{-4}}-14{{x}^{-3}}\] \[=-2\left( \frac{3}{{{x}^{4}}}+\frac{7}{{{x}^{3}}} \right)=\frac{-2}{{{x}^{4}}}(3+7x)\]

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