Question

If y = `sqrt("e"^x + sqrt("e"^x + sqrt("e"^x + .... oo)`, then `("d"y)/("d"x)` is equal to ______.

Options

• `(x"e"^x)/(2y - 1)`

• `"e"^x/(2y + 1)`

• `"e"^x/(2y - x)`

• `"e"^x/(2y - 1)`

Answer 1

If y = `sqrt("e"^x + sqrt("e"^x + sqrt("e"^x + .... oo)`, then `("d"y)/("d"x)` is equal to `"e"^x/(2y - 1)`.

Explanation:

If y = `sqrt("f"(x) + sqrt("f"(x) + sqrt("f"(x) + .... oo))` then `("d"y)/("d"x) = ("f'"(x))/(2y - 1)`

∴ `("d"y)/("d"x) = "e"^x/((2y - 1))`