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JEE Main & Advanced Mathematics Differentiation Question Bank Differentiation by Substitution

  • question_answer
    The differential coefficient of  \[{{x}^{6}}\] with respect to \[{{x}^{3}}\] is                                  [EAMCET 1988; UPSEAT 2000]

    A)            \[5{{x}^{2}}\]

    B)            \[3{{x}^{3}}\]

    C)            \[5{{x}^{5}}\]

    D)            \[2{{x}^{3}}\]

    Correct Answer: D

    Solution :

               Let \[y={{x}^{6}}\]and\[z={{x}^{3}}\]; \[\therefore \frac{dy}{dz}=\frac{dy/dx}{dz/dx}=\frac{6{{x}^{5}}}{3{{x}^{2}}}=2{{x}^{3}}\] .


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