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JEE Main & Advanced Mathematics Differentiation Question Bank Differentiation of implicit function Parametric

  • question_answer
     If \[{{\sin }^{2}}x+2\cos y+xy=0\], then \[\frac{dy}{dx}=\] [AI CBSE 1980]

    A)            \[\frac{y+2\sin x}{2\sin y+x}\]

    B)            \[\frac{y+\sin 2x}{2\sin y-x}\]

    C)            \[\frac{y+2\sin x}{\sin y+x}\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[{{\sin }^{2}}x+2\cos y+xy=0\]                    \[\Rightarrow 2\sin x\cos x-2\sin y\frac{dy}{dx}+y+x\frac{dy}{dx}=0\]                    \[\therefore \frac{dy}{dx}=\frac{y+\sin 2x}{2\sin y-x}\].


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