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

  • question_answer
    If \[{{x}^{m}}{{y}^{n}}={{(x+y)}^{m+n}}\]then \[{{\left. \frac{dy}{dx} \right|}_{x=1,y=2}}\] is equal to            [J & K 2005]

    A)            ½

    B)            2

    C)            2m/n

    D)            m/ 2n

    Correct Answer: B

    Solution :

               \[{{x}^{m}}{{y}^{n}}={{(x+y)}^{m+n}}\]               \[{{x}^{m}}.(n{{y}^{n-1}}).\frac{dy}{dx}+{{y}^{n}}(m{{x}^{m-1}})=(m+n)\,{{(x+y)}^{m+n-1}}\]\[\left( 1+\frac{dy}{dx} \right)\]                    After solving, we find \[\frac{dy}{dx}=\frac{y}{x}\] and \[{{\left. \frac{dy}{dx} \right|}_{x=1,\,y=2}}=\frac{2}{1}=2\].


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