1001_2.3_Lab_6

1001_2.3_Lab_6 - Find " f ( x ) for the...

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CALCULUS 1 LAB 6 NAME: ___________________PARTNER: _________________ 2.3 Techniques of Differentiation; GSA:______________________Lab Time: ____________ Higher Order Derivatives Useful Formulas: from 2.3 and 2.4 1. d dx [ n x ]= 1 ! n nx 2. d dx [c] = 0 3. d dx [ ) ( x cf ]= c d dx [ f ( x )] = c " f ( x ) 4. d 2 dx 2 y ( ) = d 2 y dx 2 = f (2) ( x ) = " " f ( x ) = " f ( x ) ( ) " 5. d dx [ f ( x ) ± g ( x ) ]= d dx [ f ( x )] ± d dx [ g ( x )] = " f ( x ) ± " g ( x ) 6. d n dx n y ( ) = d n y dx n = f ( n ) ( x ) Product Rule: d dx [ f ( x ) g ( x )] = g ( x ) d dx [ f ( x )] + f ( x ) d dx [ g ( x )] = g " f + f " g ; d dx ( uv ) = v du dx + u dv dx = v " u + u " v Quotient Rule: d dx [ f ( x ) g ( x ) ] = g ( x ) d dx [ f ( x )] " f ( x ) d dx [ g ( x )] [ g ( x )] 2 = g " f # f " g g 2 1. Find dx dy for the following: a. 4 5 x y = b. y = 7 x 3 + 9 x c. y = 5 " 4 + 7 x dy dx = dx dy = dx dy = 2.
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Unformatted text preview: Find " f ( x ) for the following: a. f ( x ) = 3 x " 3 + 2 x 5 b. f ( x ) = 2 x + 4 x 3 c. f ( x ) = 5 x 7 + 2 x x 2 " f x ( ) = " f x ( ) = " f x ( ) = 3. Find dt dx for the following: a. t t x 7 3 3 + = b. 1 = x c. x = 2 t + 4 t 3 dt dx = dt dx = dt dx = 4. Find d 2 y dx 2 for: a. y = 5 x 3 + 3 x 2 " 9 b. y = ( x 3 " 5)(2 x + 3) 5. Find " " " y for: y = x 4 " 5 x 2 + x...
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This note was uploaded on 02/21/2012 for the course MATH 1001 taught by Professor Dr.shaw during the Spring '11 term at FIT.

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