Differentiate the following w.r.t. x:
`(xcosx)^x+(xsinx)^(1/x)`

Explanation

To differentiate the function \( y = (x \cos x)^x + (x \sin x)^{\frac{1}{x}} \) with respect to \( x \), we will break it down into two parts: \( u = (x \cos x)^x \) and \( v = (x \sin x)^{\frac{1}{x}} \). We will find \( \frac{dy}{dx} = \frac{du}{dx} + \frac{dv}{dx} \).

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

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