Differentiate the following functions with respect to `x` : `(e^x-tanx)/(cotx-x^n)`

Explanation

To differentiate the function \( f(x) = \frac{e^x - \tan x}{\cot x - x^n} \) with respect to \( x \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), then the derivative is given by:

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

where \( u = e^x - \tan x \) and \( v = \cot x - x^n \).

...