Parametric tangent
A path is x=t^2+1, y=t^3-t. Then dy/dx=(dy/dt)/(dx/dt)=(3t^2-1)/(2t).
- Differentiate both coordinates.
- Divide only when dx/dt is nonzero.
- Evaluate at t=1.
parametric, polar, and vector representations
A path is x=t^2+1, y=t^3-t. Then dy/dx=(dy/dt)/(dx/dt)=(3t^2-1)/(2t).
Pause. Find what matters. Then make your move.