Concept of a derivative

What’s a Derivative?

A more helpful question may be

“What question does a derivative answer?”

Suppose the a variable y depends on x (so that y is a function of x).

Question: If x changes from 102 to 103.4, how much does y change?

Answer: You need the derivative.

Change in y \approx (Derivative) \times (Change in x)

We have

(Change in x)  = \Delta x = 103.4-102 = 1.4.

Therefore

(Change in y) = Derivative  \times 1.4.