State the three forms of the Product Rule for vector-valued functions.

The derivative of a vector-valued function is defined as the limit of the difference quotient, just as in the scalar-valued case.

There are two Chain Rules for vector-valued functions: one for the composite of two vector-valued functions and one for the composite of a vector-valued and a scalar-valued function.

The terms “velocity vector” and “tangent vector” for a path r(t) mean one and the same thing.

The derivative of a vector-valued function is the slope of the tangent line, just as in the scalar case.

The derivative of the cross product is the cross product of the derivatives.

State whether the following derivatives of vector-valued functions r₁(t) and r₂(t) are scalars or vectors: