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12th Class Mathematics Applications of Derivatives Question Bank Case Based (MCQs) - Derivatives

  • question_answer
    If \[u={{x}^{2}}+{{y}^{2}}\] and \[x=s+3t\], \[y=2s-t\], then \[\frac{{{d}^{2}}u}{d{{s}^{2}}}\] is equal to

    A) 12

    B) 32

    C) 36

    D) 10

    Correct Answer: D

    Solution :

    Given, \[x=s+3t,\,y=2s-t\] \[\Rightarrow \,\,\frac{dx}{ds}=1,\,\frac{dy}{ds}=2\] Now, \[u={{x}^{2}}+{{y}^{2}}\Rightarrow \frac{du}{ds}=2x\frac{dx}{ds}+2y\frac{dy}{ds}=2x+4y\] \[\Rightarrow \,\frac{{{d}^{2}}u}{d{{s}^{2}}}=2\left( \frac{dx}{ds} \right)+\left( \frac{dy}{ds} \right)\] \[\Rightarrow \,\frac{{{d}^{2}}u}{d{{s}^{2}}}=2\left( 1 \right)+4\left( 2 \right)=10\]


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