Question

y = `2sqrt(cotx^2)`

Options

• cosec²x

• `(-2x)/sqrt(cot x^2) -> "cosec"^2x`

• `sqrt(cot x^2)`

• Zero

Answer 1

`(-2x)/sqrt(cot x^2) -> "cosec"^2x`

Explanation:

Let `x^2 = t, cot t = s`

∴ `y = 2sqrt(5) = 2s 1/2`

`(dy)/(ds) = 2 * 1/2 s^(1/2 - 1) = s^(1/2) = 1/sqrt(5)`

= `(ds)/(dt) = - "cosec"^2t, (dt)/(dx)` = 2

`(dy)/(dx) = (dy)/(ds) xx (ds)/(dt) xx (dt)/(dx) = 1/sqrt(5) xx (- "cosec"^2t) xx 2x`

= `(-2x)/sqrt(cot t) = "cosec"^2t`

= `- (2x)/sqrt(cot x^2)  "cosec"^2 x^2`