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Unformatted text preview: Problem Set #1 This problem set is designed to give you a little bit of practice in comput- ing derivatives and solving some simple optimization problems. The focus of much of the problem set is on the power rule of differentiation, use of the (natural) logarithm, and taking derivatives of the logarithm of a given function. 1 Derivatives Find the derivatives of the following functions. 1. f ( x ) = x 8 2. f ( x ) = x 2 (1 + 2 x ) 3. f ( x ) = 4 x 1 2 4. f ( x ) = x- 1 3 5. f ( x ) = 5ln x . 6. f ( x ) = 4 x x- 2 7. f ( x ) = 15 x 2 + x 3 8. f ( x ) = e 2 x , where e is the base of the natural logs. 9. f ( x ) = ( x + ln x )(3 x- x 2 ) 10. f ( x ) = ( ax- b ) cx 2 , for constants a, b, and c . 11. f ( x ) = ax b , for constants a and b . 12. Consider the function ax b again. What is the derivative of the natural logarithm of this function? 13. Once again, consider the function ax b . What if you take the derivative of this function, and then compute the quantity f ′ ( x ) f ( x ) ? (That is, the derivative of the function divided by the function itself). 1 2 Partial Derivatives For the following functions, find the partial derivatives with respect to both x and y ....
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This note was uploaded on 11/12/2009 for the course ECONOMICS 701 taught by Professor Baker during the Spring '09 term at CUNY Hunter.
- Spring '09