Answer
$\dfrac{e^x|x+2|}{[1+(xe^x+e^x)^2]^{3/2}}$
Work Step by Step
Given: $y=xe^x$
Consider $f(x)=y=xe^x$
In order to find the curvature we will have to use formula 11, such that
$\kappa(x)=\dfrac{|f''(x)|}{[1+(f'(x))^2]^{3/2}}$
$y'=e^x+xe^x$
and $y''=e^x(2+x)$
$\kappa(x)=\dfrac{|e^x(2+x)|}{[1+(1+x)e^x)^2]^{3/2}}$
Hence, $\kappa(x)=\dfrac{e^x|x+2|}{[1+(xe^x+e^x)^2]^{3/2}}$
