If `y=x^x+x^(1//x)` , find `(dy)/(dx)`

Explanation

To find the derivative \( \frac{dy}{dx} \) of the function \( y = x^x + x^{\frac{1}{x}} \), we can break it down into two parts: \( u = x^x \) and \( v = x^{\frac{1}{x}} \). We will find \( \frac{du}{dx} \) and \( \frac{dv}{dx} \) separately and then combine them.

### Step 1: Differentiate \( u = x^x \)

1. Take the natural logarithm of both sides:
\[ \log u = \log(x^x) = x \log x \]
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