Question

2.
$\frac{d}{dx}(xe^{\ln x^{2}})=$

Explanation:

Step1: Simplify the function

First, simplify \(e^{\ln x^{2}}\) using the property \(e^{\ln a}=a\) (\(a>0\)). So \(e^{\ln x^{2}} = x^{2}\), and the function becomes \(y = x\cdot x^{2}=x^{3}\).

Step2: Differentiate the simplified function

Differentiate \(y = x^{3}\) using the power rule \(\frac{d}{dx}(x^{n})=nx^{n - 1}\). Here \(n = 3\), so \(\frac{dy}{dx}=\frac{d}{dx}(x^{3})\).

Answer:

\(3x^{2}\)