Question

y = `cos sqrt(x)`

Options

• `- 1/(2sqrt(x)) sin sqrt(x)`

• `(- sin t) 1/(2sqrt(x)`

• `- 1/(2sqrt(x)) cos sqrt(x)`

• Both `- 1/(2sqrt(x)) sin sqrt(x)` and `(- sin t) 1/(2sqrt(x)`

Answer 1

Both `- 1/(2sqrt(x)) sin sqrt(x)` and `(- sin t) 1/(2sqrt(x)`

Explanation:

`y = cos sqrt(x)`, put `sqrt(x) = t`

`y = cos t, t = sqrt(x)`

`(dy)/(dt) = - sin t, (dt)/(dx) = 1/2 x^(1/2 - 1) = 1/(2sqrt(x))`

∴ `(dy)/(dx) = (dy)/(dt) xx (dt)/(dx) = (- sin t) 1/(2sqrt(x)) = - 1/(2sqrt(x)) sin sqrt(x)`