# How do you differentiate g(x) = xe^(2x)lnx using the product rule?

The product rule for three functions $f , g , h$ is as follows
$\left(f \cdot g \cdot h\right) ' = \frac{\mathrm{df}}{\mathrm{dx}} \cdot g \cdot h + f \cdot \frac{\mathrm{dg}}{\mathrm{dx}} \cdot h + f \cdot g \cdot \frac{\mathrm{dh}}{\mathrm{dx}}$
$\frac{d}{\mathrm{dx}} \left(x {e}^{2 x} \ln \left(x\right)\right) = {e}^{2 x} \left(2 x \ln \left(x\right) + \ln \left(x\right) + 1\right)$