Question

If xy = tan^–1 (xy) + cot^–1 (xy), then `(dy/dx)_((4","  2))` = ______.

where (x, y) ∈ R

Options

• `1/2`

• –2

• 2

• `(-1)/2`

Answer 1

If xy = tan^–1 (xy) + cot^–1 (xy), then `(dy/dx)_((4","  2))` = `underlinebb((-1)/2)`.

where (x, y) ∈ R

Explanation:

Given, xy = tan^–1 (xy) + cot^–1 (xy)

`\implies` xy = `π/2`  ...`[∵ tan^-1x + cot^-1x = π/2]`  ...(i)

Now, differentiating, both sides of equation (i), we get

`x dy/dx + y` = 0

`\implies dy/dx = (-y)/x`

`\implies (dy/dx)_((4"," 2)) = (-2)/4 = (-1)/2`