Derivatives describe the *rate* at which things change. The derivative is defined as

(We will use this definition when deriving transmission line equations at the end of this chapter.)

Let *y* be the function of *x*, that is, *y* = *f* (*x*). We often use the shorthand notation *y′* or *f ′*(*x*) to denote the derivative of *y* (Simon, 1982, p. 115). This notation does not indicate the variable with respect to which the derivative is evaluated (*y* could be a function not only of *x* but also of other variables). In many applications, it is important to identify that variable. We therefore use the alternative notation or to indicate that derivative of *y* is computed with respect to the variable *x*.

Computing derivatives using the definition (3.1) can be tedious. Fortunately, such computations are usually unnecessary because there are derivative formulas that enable us to find the derivatives without computing limits.

Next we will state several useful formulas for derivatives

(3.2a)

(3.2b)

(3.2c)

(3.2d)

(3.2e)

(3.2f)

(3.2g)

(3.2h)

(3.2i)

(3.2j)

(3.3a)

(3.3b)

(3.3d) ...

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