The Tangent(f, var) command computes the object tangent to the parameterized curve or surface f at the point specified in the other arguments var. Tangent is a generic command that can accept the parameters of both TangentLine and TangentPlane, except scalar expressions.

If f is a Vector, the extra arguments must be equations, since the parameter names are required in this case.

If f is a Vector-valued procedure, the parameter names can be omitted, but the extra arguments must all be the same type, either algebraic expressions or equations.

If f is a Vector, the output will be a position Vector describing the object tangent to f at the point specified by the other parameters var; this position Vector will use parameter variable names specified in var.

If f is a Vector-valued procedure, the output will be a procedure, and will use _t, , as its parameter names, where  is the number of parameters in f. This output procedure evaluates to a position Vector.

The input Vector is a representation of the graph of the object in question. For example, to calculate the tangent plane to the function f := x^2+y^2, the function should be entered as the Vector <x, y, x^2+y^2>, where x and y are the parameters.