Official solution
y = xex2
\[{\left. {{{dy} \over {dx}}} \right|_{(1,e)}}{\left. { = \left( {e.e{x^2}.2x + {e^{{x^2}}}} \right)} \right|_{(1,e)}}\]
\[ = 2 \cdot e + e = 3e\]
T : y - e = 3e (x - 1)
y = 3ex - 3e + e
y = \[\left( {3e} \right)x - 2e\]
\[\left( {{4 \over 3},2e} \right)\] lies on it