Home
Class 12
MATHS
If y= sqrt (log x + sqrt (log x + sqrt (...

If `y= sqrt (log x + sqrt (log x + sqrt (log x + ......oo)))`, then show that `dy/dx = frac{1}{x(2y-1)}`

A

`x/(2y-1)`

B

`x/(2y+1)`

C

`1/(2y-x)`

D

`1/(x(2y-1))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

If y= sqrt (cos x + sqrt (cos x + sqrt (cos x + ......oo))) , then show that dy/dx = frac{sin x}{1-2y}

If y= sqrt (log x + sqrt (log x + sqrt (log x + .......oo))) , then dy/dx =....... A) frac{1}{2y-1} B) frac {1}{x(2y-1)} C) frac {1}{2xy} D) frac {1}{x(y-1)}

If y= sqrt (sin x + sqrt (sin x + sqrt (sin x + .......oo))) , then show that dy/dx = frac {cos x}{2y-1}

If y= x^(x^(x...)) , then show that dy/dx = frac{y^2}{x(1-log y)}

If x = e^(x/y) , then show that dy/dx = frac{x-y}{x log x}

If x^y = e^(x-y) , then show that dy/dx = frac{log x}{(1+ log x)^2}

If sqrt (y+x) + sqrt (y-x) = c , then show that dy/dx = frac{y}{x} - sqrt (frac{y^2}{x^2} -1)

If sqrt (1- x^2 ) + sqrt (1- y^2 ) = a(x-y), then show that dy/dx = sqrt ( frac{1- y^2 }{1- x^2 } )

If e^y = y^x , then show that dy/dx = frac{(log y)^2}{log y -1}