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3-59.

MORE NOTABLE NOTATION FOR THE DERIVATIVE

The use of comes from , which is an expression for slope read as “the change in y over the change in ”. We use to represent change. When the change gets smaller and smaller until it is infinitely small (infinitesimal) we use the symbol .

It is useful to think of change when working with derivatives. For example  can represent the change in the height of an object with respect to time. Create expressions using the symbol  that represent the following instantaneous change statements. Homework Help ✎

  1. The change in the velocity, , with respect to time.

    instantaneous acceleration  

  2. The change in volume, V, with respect to the radius, , of a cone.

  3. The change in area, , of a circle with respect to the perimeter, .