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  • Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 22

Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 22

Answers (1)

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Answer: The value of   \frac{d y}{d x}=\frac{1}{(1-x)^{2}}

Hint:

we replace 1+x+x^{2}+\cdots \infty \text { by } \frac{1}{1-x}

Given:

|x|<1 \text { and } y=1+x+x^{2}+\cdots \infty
Solution:  

Since  |x|<1,

\begin{aligned} &y=1+x+x^{2}+\cdots \infty \\\\ &=\frac{1}{1-x} \\\\ &\therefore \frac{d y}{d x}=-\frac{1}{(1-x)^{2}} \cdot-1 \end{aligned}

       \frac{d y}{d x}=\frac{1}{(1-x)^{2}}

 

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