Differentiate the following function with respect of `x :(a+sinx)/(1+asinx)`

Explanation

u = a + sin x and v = 1 + a sin x

∴ y = u/v

As, u = a + sin x

du/dx=cosx

As, v = 1 + a sin x

dv/dx=acosx

Thus,`dy/dx=(v(du/dx)-u(dv/dx))/v^2`

`dy/dx=cosx(1-a^2)/(1+asinx)^2`