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# Derivatives.

Definition 2.11   The function is differentiable at t0 if there exists a vector such that

We denote:

Proposition 2.12   The function is differentiable at t0 if, and only if each component fi is differentiable at t0. We have:

Example 2.13   If , then

.

Definition 2.14   With the notations of  refdef derivation. Let the function describe the motion of a particle.
1.
The vector is the velocity vector of the particle at time t0.
2.
The number is the speed of the particle at t0.

Definition 2.15   With the same notations. The acceleration at t0 is the derivative of at t0. we denote it by .

Example 2.16   Let . Then:

• Velocity: .
• Acceleration: .
Please check that, in this example, are orthogonal for every value of t.

Noah Dana-Picard
2001-05-30