Question

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+....oo))),` then `dy/dx` equals ______.

विकल्प

• `cosx/(2y-1)`

• `sinx/(1-2y)`

• `sinx/(1+2y)`

• `cosx/(1-2y)`

Answer 1

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+....oo))),` then `dy/dx` equals `underline(cosx/(2y-1))`.

Explanation:

If `y=sqrt(f(x)+sqrt(f(x)+sqrt(f(x)+....oo))),` then 

`dy/dx=(f^'(x))/(2y-1)`

`thereforedy/dx=cosx/(2y-1)`