Waves/Derivatives

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Math Tutorial -- DerivativesEdit

Figure 1.15: Estimation of the derivative
Figure 1.15: Estimation of the derivative, which is the slope of the tangent line. When point B approaches point A, the slope of the line AB approaches the slope of the tangent to the curve at point A.

This section provides a quick introduction to the idea of the derivative. For a more detailed discussion and exploration of the differentiation and of Calculus, see Calculus and Differentiation.

Often we are interested in the slope of a line tangent to a function at some value of . This slope is called the derivative and is denoted . Since a tangent line to the function can be defined at any point , the derivative itself is a function of :

(2.25)

As figure 1.15 illustrates, the slope of the tangent line at some point on the function may be approximated by the slope of a line connecting two points, A and B, set a finite distance apart on the curve:

(2.26)

As B is moved closer to A, the approximation becomes better. In the limit when B moves infinitely close to A, it is exact.

Table of DerivativesEdit

Derivatives of some common functions are now given. In each case is a constant.


Table of Derivatives
where both xc and cxc-1 are defined.
x > 0
c > 0</math>
c > 0,

The product and chain rules are used to compute the derivatives of complex functions. For instance,

and


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