Differentiate the following functions with respect to `x` : `(x+e^x)/(1+logx)`

Explanation

To differentiate the function \( y = \frac{x + e^x}{1 + \log x} \) with respect to \( x \), we will use the quotient rule. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), then the derivative \( \frac{dy}{dx} \) is given by:

\[ \frac{dy}{dx} = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} \]

where \( u = x + e^x \) and \( v = 1 + \log x \).

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