UFCalcSet16 - Exercises UF Calculus Set 16 1. Write dy du...

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UF Calculus Set 16 1. Write dy du and du dx . Then, differentiate y with respect to x by employing chain rule: (a) y = u - 1 / 2 where u = 5 x + 4 (b) y = u 5 where u = 2 - x 3 2. Find the derivative of the given function; state the domain of f and its derivative. (a) f ( x ) = (1 - 4 x 3 ) - 2 (b) f ( x ) = 100(100 - x 2 ) 3 / 2 (c) f ( x ) = sin 2 ( x ) (d) f ( x ) = e sin( x ) (e) f ( x ) = 1 p 5 - x (f) f ( x ) = (2 x 2 + 1) 3 ( x 2 - 1) 2 (g) f ( x ) = x 2 (1 - x ) 1 / 3 (h) f ( x ) = x 2 e - x (i) f ( x ) = ( e x + e - x ) 2 2 e x (j) f ( x ) = 3 x 2 3. For each function above, find all x -values at which the function has horizontal tangent lines. 4. Calculate the second derivative of the functions (a) f ( θ ) = sec 2 (3 θ ) (b) f ( t ) = t 1 + t 2 (c) f ( θ ) = (4 - 2 x 2 ) 10 5. Use the table above without context. Find the value of the derivative of each of the following functions at t = 1 , 4 : (a) ( V A )( t ) (b) ( A A )( t ) (c) A ( t ) (d) [ t
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This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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UFCalcSet16 - Exercises UF Calculus Set 16 1. Write dy du...

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