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  • Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 46

Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 46

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Answer: \frac{d y}{d x}=\frac{\sin ^{2}(a+y)}{\sin (a+y)-y \cos (a+y)}

Hint: To solve this equation we use uv'  form

Given: y=x \sin (a+y)

Solution:  

        (u v)^{\prime}=u^{\prime} v+v^{\prime} u

        \begin{aligned} &\frac{d y}{d x}=1 \times \sin (a+y)+x \cos (a+y)\left[0+\frac{d y}{d x}\right] \\\\ &y^{\prime}=\sin (a+y)+x \cos (a+y) y^{\prime} \end{aligned}

        \begin{aligned} &y^{\prime}=\frac{\sin (a+y)}{1-x \cos (a+y)} \cdot \frac{\sin (a+y)}{\sin (a+y)} \\\\ &\frac{d y}{d x}=\frac{\sin ^{2}(a+y)}{\sin (a+y)-y \cdot \cos (a+y)} \end{aligned}

Hence proved

 

Posted by

infoexpert26

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