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Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 50

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Answer:  \frac{d y}{d x}=\frac{y}{x(1-x \cos y)}

Hint: To solve this equation we differentiate it separately

Given: y=x \sin y

Solution:  

        y=x \sin y

        \begin{aligned} &u=x-1 \\ &v=\sin y \end{aligned}

        \begin{aligned} &\frac{d y}{d x}=x \cos y \frac{d y}{d x}+\sin y \cdot 1 \\\\ &\frac{d y}{d x}=x \cos y \frac{d y}{d x}+\sin y \end{aligned}

        \begin{aligned} &\frac{d y}{d x}-x \cos y \frac{d y}{d x}=\sin y \\\\ &\frac{d y}{d x}(1-x \cos y)=\sin y \\\\ &\frac{d y}{d x}=\frac{y}{x(1-x \cos y)} \end{aligned}

Hence proved

 

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