I am taking AP physics and I am generally confused about work and power. We are using all sorts of derivatives and integrals and I don't understand how to do them. Could some one please help me figure this out?

Power is defined as work per unit time. Since work is force times distance, this means that for a constant force power is force times velocity. Stated another way, power is the derivative of work per unit time, and work is the integral of power over time. We can help better if you gave us an example of a particular problem that has you baffled.

To clarify further:

WORK: Multiply the component of force in the direction of motion, by distance moved.

If you are familiar with Vectors,

Work = Dot product of Force-vector and distance-vector

Remember: No motion, no WORK!