Differentiate the following functions with respect to `(x^2+2)/(sqrt(cosx))`

Explanation

Here, we will use,

`(u/v)' = (u'v-v'u)/v^2`
Let `y = (x^2+2)/(sqrtcosx)`

Differntiating both sides w.r.t. `x`,

`dy/dx = ((2x)sqrt(cosx) - (1/(2sqrtcosx))(-sinx)(x^2+2))/cosx`

`=>dy/dx = (4xcosx+sinx(x^2+2))/(2cosxsqrtcosx)`

`=>dy/dx = (2x)/sqrtcosx +(tanx(x^2+2))/(2sqrtcosx)`, which is the required solution.