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Applied Mathematics, Calculus, and Differential Equations 219

Figure 3.5 Full-rectified sine
wave.

as shown in Fig. 3.6. Let x represent a small change in x, and
let y represent the change in y f(x) that occurð as a result
of x. Then the derivative of f at (x ,y ) is defined as:
0 0
f (x ) Lim x→0 ( y/ x)
0
If f is differentiable at all pointð in itð domain, then the deriv-
ative of f is defined and can be denoted in several ways:

f (x) d/dx ( f ) df/dx dy/dx

In Fig. 3.6, the slope of line L approacheð f (x )as x → 0.
0

Figure 3.6 Derivative repre-
sented by the slope of a
curve at a point.