Answer: \(\mathrm{e}^{3x}(2x+3x^2)\).

Use the product rule for

\(x^2\mathrm e^{3x}.\)

Let

\(u=x^2,\qquad v=\mathrm e^{3x}.\)

Then

\(u'=2x,\qquad v'=3\mathrm e^{3x}.\)

Therefore

\(\dfrac{\mathrm d}{\mathrm dx}\left(x^2\mathrm e^{3x}\right)=2x\mathrm e^{3x}+x^2(3\mathrm e^{3x}).\)

Factorising \(\mathrm e^{3x}\),

\(\dfrac{\mathrm d}{\mathrm dx}\left(x^2\mathrm e^{3x}\right)=\mathrm e^{3x}(2x+3x^2).\)