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

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

Answers (1)

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

 

Posted by

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