3 A curve has equation \(y = x ^ { 3 } \ln x\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Find an equation of the tangent to the curve \(y = x ^ { 3 } \ln x\) at the point on the curve where \(x = \mathrm { e }\).
- This tangent intersects the \(x\)-axis at the point \(A\). Find the exact value of the \(x\)-coordinate of the point \(A\).