notes-five-rules-derivatives

notes-five-rules-derivatives - 1 1.1 Derivatives: The Five...

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1 Derivatives: The Five Basic Rules 1.1 Nonlinear Functions The term derivative means ”slope” or rate of change. The f ve rules we are about to learn allow us to f nd the slope of about 90% of functions used in economics, business, and social sciences. Suppose we have a function y = f ( x ) (1) where f ( x ) is a non linear function. For example: 1 y = x 2 2 y =3 x x 1 / 2 3 y = ax + bx 2 + c (2) Each equation is illustrated in Figure 1. 1.2 The Derivative Given the general function y = f ( x ) the derivative of y is denoted as dy dx = f 0 ( x )( = y 0 ) The symbol dy dx is an abbreviation for ”the change in y ( dy ) FROM a change in x ( dx )”; or the ”rise over the run”. In other words, the slope. 1.3 The Five Rules 1.3.1 The Constant Rule Given y = f ( x )= c, where c is an arbitrary constant, then dy dx = f 0 ( x )=0 (3) 1.3.2 Power Function Rule Suppose y = ax n (4) where a and n are any two constants. The power function rule states that the slope of the function is given by dy dx = f 0 ( x anx n 1 (5) 1
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yy y x x Y = x 2 Y = x 1/2 x Y = ax 2 + bx +c Examples of common nonlinear functions Figure 1: 2
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notes-five-rules-derivatives - 1 1.1 Derivatives: The Five...

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