Question

If y = sin^–1x, then (1 – x²)y₂ is equal to ______.

Options

• xy₁

• xy

• xy₂

• x²

Answer 1

If y = sin^–1x, then (1 – x²)y₂ is equal to `underline(bb(xy_1))`.

Explanation:

y = sin^–1x

`(dy)/(dx) = 1/sqrt(1 - x^2)`

⇒ `sqrt(1 - x^2) . (dy)/(dx)` = 1

Again, differentiating both sides w. r. to x, we get

`sqrt(1 - x^2) (d^2y)/(dx^2) + (dy)/(dx) . ((-2x)/(2sqrt(1 - x^2)))` = 0

Simplifying, we get (1 – x²)y₂ = xy₁