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How can you determine the derivative of [math]x \ln x[/math]?
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To find the derivative of [math]x\ln x[/math], we can use the product rule of differentiation. Let [math]u=x[/math] and [math]v=\ln x[/math]. Then we have [math]y=uv[/math]. Taking the derivative of both sides with respect to [math]x[/math], we get [math]\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}[/math]. Substituting [math]u=x[/math] and [math]v=\ln x[/math], we get [math]\frac{dy}{dx} = x\frac{1}{x} + \ln x \cdot 1[/math]. Simplifying this expression gives us [math]\frac{dy}{dx} = \ln x + 1[/math].