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  • Please solve RD Sharma class 12 chapter Differentiation exercise 10.5 question 45 maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.5 question 45 maths textbook solution

Answers (1)

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

Hint: To solve this equation we will convert term into log

Given: e^{x+y}-x=0

Solution:  

        e^{x+y}-x=0

        \begin{aligned} &\log e^{x+y}=\log x \\\\ &(x+y) \log e=\log x \\\\ &\frac{d}{d x}(x+y)=\frac{d}{d x}(\log x) \end{aligned}

        \begin{aligned} &1+\frac{d y}{d x}=\frac{1}{x} \\\\ &\frac{d y}{d x}=\frac{1}{x}-1=\frac{1-x}{x} \\\\ &\frac{d y}{d x}=\frac{1-x}{x} \end{aligned}

Hence proved

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