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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

Answers (1)

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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