Question

If y = `x^3 + 1/(x^3 + 1/(x^3 + 1/(x^3 + .....oo)`, ten `("d"y)/("d"x)` = ______.

Options

• `(3x^2y)/(2y - x^3)`

• `(x^3y)/(y + x^3)`

• `(x^3y)/(y - x^3)`

• `(3x^2y)/(2 + x^3/y)`

Answer 1

If y = `x^3 + 1/(x^3 + 1/(x^3 + 1/(x^3 + .....oo)`, ten `("d"y)/("d"x)` = `(3x^2y)/(2y - x^3)`.

Explanation:

y = `x^3 + 1/y`

if y = f(x) + `1/y`, tthen `("d"y)/("d"x) = (y"f'"(x))/(2y - "f"(x))`

∴ `("d"y)/("d"x) = (3x^2y)/(2y - x^3)`