First Derivative

Calculus Level 3

$y=\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-\cdots}}}}$ Your task is to find the first derivative of $y$ and submit your answer as $y'(1)$ .

The answer is 1.

1 solution

Reynan Henry
Dec 26, 2016

first we find $y$ when $x=1$ $y=\sqrt{1+\sqrt{1-\sqrt{1+\cdots}}}=\sqrt{1+\sqrt{1-y}}$ or $y^4-2y^2+y=0$ which give us $y=1$

second we find the derivative $y=\sqrt{x+\sqrt{x-y}}$ or $x-y=(y^2-x)^2\Rightarrow$ $1-y'=2(y^2-x)(2y\cdot y'-1)$ then we substitue $x=1,y=1$ and we get $1-y'=0$ or $y'=1$

@Reynan Henry - If you could just elaborate the solution , It would be just brilliant . But I must still say it deserves a upvote

Anubhav Tyagi - 4 years, 5 months ago

Yeah! I also solve by same way..

Prokash Shakkhar - 4 years, 5 months ago

First Derivative

The answer is 1.

1 solution

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