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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

Answers (1)

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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