# Deriv - Derivative Review and Practice Handout Economics...

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Derivative Review and Practice Handout Economics 301: Intermediate Microeconomic Theory Korinna K. Hansen Functions with One Variable For taking derivatives you will need to remember some basic equation properties and calculus rules. Here are some important properties and rules: e a+b = e a e b (e a ) b = e ab ln (x a ) = a lnx ln (xy) = lnx + lny If b is a constant, then dx d b = 0 and dx )) ( ( d x f b =b f (x). The Power Rule: If n is a positive integer, then dx ) d(x n = n x n-1 The Chain Rule: For a function of a function h(x) = g(f(x)) we know that the derivative dh(x)/dx = g (f(x)) f (x). The Product Rule: For a function h(x) = f(x) g(x) we know that the derivative dx dh(x) = dx g(x)) f(x) ( d = g(x) dx df(x) + f(x) dx dg(x) = g(x) f (x) + f(x) g (x). The Quotient Rule: dx dh(x) = dx g(x)) / f(x) ( d = 2 ) ( ) / ) ( )( ( ) / ) ( )( ( x g dx x dg x f dx x df x g - Find the derivatives of the following functions. Solutions follow on the right half of this page. 1. h(x) = 4x 3 +3x 2 +x +5 h (x) = 12x 2 + 6x +1 2. h(x) = (4x 2 - 1) (7x 3 + x) h (x) = (4x 2 – 1) (21x 2 +1) + (7x 3 + x) (8x) 3. h(x) = (1 + x 2 ) 2 h (x) = 2(1+x 2 ) 2x 4. h(x) = x 2 + 1/x h

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