Question

y = cos (sin x)

Options

• `- sin t`

• `cos x`

• `-[sin(sin x)] cos x`

• `tan x`

Answer 1

`-[sin(sin x)] cos x`

Explanation:

Let, `y = cos (sin x)`

Put `sin x = t`,

∴ `y = cost, t = sin x`

∴ `(dt)/(dx) = - sin t, (dt)/(dx) = cos x`

`(dy)/(dx) = (dy)/(dt) * (dt)/(dx) = (- sin t) xx (cos x)`

Putting value of `t`,

`(dy)/(dx) = - sin(sin x) xx cos x`

= `-[sin(sin x)] cos x`.