Question

Let y = `cot^-1((5x^2 + 1)/(4x)) + cot^-1((2x - 3)/(2 + 3x))`, then `dy/dx` = ______ 

विकल्प

• `1/(1 + 25x^2)`

• `5/(1 + 25x^2)`

• `5/sqrt(1 + 25x^2)`

• `1/(1 + 5x^2)`

Answer 1

Let y = `cot^-1((5x^2 + 1)/(4x)) + cot^-1((2x - 3)/(2 + 3x))`, then `dy/dx` = `underline(5/(1 + 25x^2))`.

Explanation:

`y = cot^-1 ((5x . x + 1)/(5x - x)) + cot^-1  ((2/3 x - 1)/(2/3 + x))`

= `tan^-1((5x - x)/(5x . x + 1)) + tan^-1 ((2/3 + x)/(2/3 x - 1))`

= `tan^-1 5x - tan^-1 x + tan^-1  2/3 + tan^-1x`

= `tan^-1 5x + tan^-1  2/3`

∴ `dy/dx = 1/(1 + (5x)^2) . 5 = 5/(1 + 25x^2)`