Differentiate the following functions with respect to `x : `x^2e^xlogx`

Explanation

To differentiate the function \( f(x) = x^2 e^{x \log x} \) with respect to \( x \), we will use the product rule and the chain rule. Here’s a step-by-step solution:

### Step 1: Identify the components of the function
The function can be rewritten as:
\[ f(x) = x^2 \cdot e^{x \log x} \]
Here, we have two parts: \( u = x^2 \) and \( v = e^{x \log x} \).
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