The answer is True.
On differentiating using product rule,
[tex]\mathsf {\frac{d}{dx}[xe^{x}] = x(e^{x})+e^{x}(1)}[/tex]
[tex]\mathsf {\frac{d}{dx}[xe^{x}] = e^{x}(x + 1)}[/tex]
The general form of product rule :
[tex]\boxed {\frac{d}{dx}(ab) = a(b')+b(a')}[/tex]
