Task: Find the derivative via the limit of the deltas.
(A delta is a small change, the in your calculations. Taken to the limit, we call it an infinitesimal, and often write it ; this is the you've seen your teacher use. refers to a finite non-zero change; you'll see that usage more often in physics.) Step 1: Limit: From the limit definition of a derivative:
Step 2: Rewrite the outer fraction as multiplication: Dividing by and multiplying by are the sam">