Find derivative of the following functions: `x/(1+tanx)`

Explanation

To find the derivative of the function \( f(x) = \frac{x}{1 + \tan x} \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form of \( \frac{u}{v} \), then the derivative is given by:

\[ \frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2} \]

where \( u \) and \( v \) are functions of \( x \), and \( u' \) and \( v' \) are their respective derivatives.

...