Differentiate `e^xlogsqrt(x)tanx` with respect to `x` .

Explanation

To differentiate the function \( y = e^x \log(\sqrt{x}) \tan(x) \) with respect to \( x \), we will apply the product rule and the chain rule. The product rule states that if you have a product of functions \( u(x) \) and \( v(x) \), then the derivative is given by:

\[ \frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x) \]

In our case, we have three functions multiplied together: \( u = e^x \), \( v = \log(\sqrt{x}) \), and \( w = \tan(x) \). Thus, we will use the product rule multiple times.

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