8 A curve has parametric equations \(x = \frac { t } { 1 + t ^ { 3 } } , y = \frac { t ^ { 2 } } { 1 + t ^ { 3 } }\), where \(t \neq - 1\).
- In this question you must show detailed reasoning.
Determine the gradient of the curve at the point where \(t = 1\).
- Verify that the cartesian equation of the curve is \(x ^ { 3 } + y ^ { 3 } = x y\).