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  • Provide solution RD Sharma maths class 12 chapter 10 differentiation exercise 10.6 question 3 maths textbook solution

    Provide solution RD Sharma maths class 12 chapter 10 differentiation exercise 10.6 question 3 maths textbook solution            

Answers (1)

Answer: \left ( 2y-1 \right )\frac{dy}{dx}=\frac{1}{x}

Hint: The value of y is given as infinite series. If a term is deleted from an infinite series, it remains the same in this case.

Given: y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+\ldots \ldots \ldots .+\infty}}}

Solution:

Here it is given that,

            y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+\ldots \ldots \ldots .+\infty}}}

This can be written as:

          y=\sqrt{\log x+y}

Squaring on both sides, we get:

        y^{2}=\left ( \log x+y \right )                                                                                …(1)

Differentiating (1) w.r.t x,

                         \begin{aligned} &2 y \frac{d y}{d x}=\frac{1}{x}+\frac{d y}{d x} \\ &\frac{d y}{d x}(2 y-1)=\frac{1}{x} \end{aligned}

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

. Hence, it is proved.

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