Q2Solutions - f ( x ) g ( x ) ) = f ( x ) g ( x ) + f ( x )...

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MAC 2233 Quiz 2 Solutions June 5, 2009 1. Let f be a function which is differentiable at a point x . Write the limit definition of f 0 ( x ), the derivative of f at x . Solution: lim x 0 f ( x + h ) - f ( x ) h 2. (a) Write the power rule for the differentiating the function f ( x ) = x n , where n is a fixed real number. Solution: f 0 ( x ) = nx n - 1 (b) Use the power rule to find the derivative of f ( x ) = 5 x . Solution: f 0 ( x ) = nx n - 1 = 1 5 x 1 - 1 5 = 1 5 x - 4 5 3. (a) Let f ( x ) and g ( x ) be differentiable functions. Write the product rule for the derivative of the product f ( x ) g ( x ). Solution: (
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Unformatted text preview: f ( x ) g ( x ) ) = f ( x ) g ( x ) + f ( x ) g ( x ) (b) Use the product rule on the functions f ( x ) = 3 x and g ( x ) = x to nd the derivative of the functions f ( x ) g ( x ) = 3 x 2 . Note: Using methods other than the product rule to nd the derivative will receive no credit, but may be useful for checking your work. Solution: ( f ( x ) g ( x ) ) = (3 x * x ) = 3 x * 1 + x * 3 = 3 x + 3 x = 6 x...
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This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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