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Home  Differentiation Derivatives of Rational Functions Corollaries |
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Corollaries
Two useful facts can be stated as corollaries. COROLLARY 1 The derivative of a polynomial of degree n > 0 is a polynomial of degree n - 1. (A nonzero constant is counted as a polynomial of degree zero.) COROLLARY 2 If u depends on x, then
whenever du/dx exists. That is, adding a constant to a function does not change its derivative. In Figure 2.3.1 we see that the effect of adding a constant is to move the curve up or down the y-axis without changing the slope.
Figure 2.3.1
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Last Update: 2006-11-05