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  • Need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 39

Need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 39

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Answer:  \frac{d y}{d x}=-\frac{m y}{n x}

Hint: To solve this we add log on both sides

Given: x^{m} y^{n}=1

Solution:  

        \log \left(x^{m} y^{n}\right)=\log 1=0

        \begin{aligned} &\log x^{m}+\log y^{n}=0 \\\\ &\frac{d}{d x} m \log x+n \log y=\frac{d}{d x} 0 \end{aligned}

        \begin{aligned} &m \cdot \frac{1}{x}+n \frac{1}{y} \frac{d y}{d x}=0 \\\\ &\frac{d y}{d x}=\frac{-m y}{n x} \end{aligned}

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