Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution RD Sharma maths class 12 chapter 10 differentiation exercise 10.6 question 1 maths textbook solution

Provide solution RD Sharma maths class 12 chapter 10 differentiation exercise 10.6 question 1 maths textbook solution

Answers (1)

Answer: \frac{d y}{d x}=\frac{1}{2 y-1}

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{x+\sqrt{x+\sqrt{x+\ldots \ldots \ldots+\infty}}}

Solution:

Here it is given that,

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

This can be written as:

        y=\sqrt{x+y}

Squaring on both sides, we get:

       y^{2}=x+y                                                                                                    …(1)

Differentiating (1) w.r.t x,

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

Hence, it is proved.

 

Posted by

Infoexpert

View full answer

Similar Questions

Latest Question