University:
Missouri State University
Course:
MTH 137 | Precalculus 2
Academic year:

2021
Views:

435

Pages:

2
Author:

Zaria Bauer

Calculus - Derivatives by Tables - 30 points - Solutions x f ( x) f "( x ) g( x ) 2 π/3 7 5 3 3 π/4 4 4 9 π/2 -3 9 4 -3 2 g"( x ) -4 ! 9 π π/2 ! For each problem, find ! the requested information. Show your steps. Answers should first be calculated exactly and then found accurate to 3 decimal places. ! Grading: • Problems are 3 pts apiece • Take one point off for each arithmetic or algebra error • Take off full credit if derivative rules weren’t applied correctly • Take off 2 points for each time chain rule wasn’t used in problems 1 • Take off point if algebra work correct but decimal answers incorrect 2 (1) d [ f ( x ) + g( x )] at x = 2 dx (2) f ( x ) " g#( x ) + g( x ) " f #( x ) f "( x ) + g"( x ) ! f ( 4 ) " g#( 4 ) + g( 4 ) " f #( 4 ) ! f "(2) + g"(2) 9 " $ + (%3) " 7#4 3 ! (3) d [ f ( x ) " g( x )] at x = 4 dx $ 2 15$ = 23.562 2 d " f ( x )% $ ' at x = 9 dx # g( x ) & (4) ! 3 d f ( x )] at x = 9 [ dx g( x ) " f #( x ) $ f ( x ) " g#( x ) ! [g( x )] 2 ! 2 3[ f ( x )] " f #( x ) g(9) " f #(9) $ f (9) " g#(9) [g(9)] 2 2 3[ f (9)] " f #(9) ( ) 2($3) $ 4 % 2 4 $6 $ 2% = $3.071 4 3(16)($3) $144 ! ! " % d$ 1 ' (6) at x = 4 dx $# f ( x ) '& d 2 (5) [x " g( x )] at x = 4 dx x 2 " g #( x ) + g ( x ) " 2x 16 g #(4) + g (4) " (8) "1 d f ( x )] 2 [ dx "3 1 "1 " [ f ( x )] 2 # f $( x ) = # f $( x ) 3 2 2[ f ( x )] 2 ! 16$ + (%3)(8) 16$ % 24 = 26.265 "1 2[9] 3 2 # f $( 4 ) = "1 % "% # = = "0.029 2(27) 2 108 ! (7) d f ( g( x )) at x = 3 dx [ ] (8) ! f "[ g( x )] # g"( x ) ! f "[ g( 3)] # g"( 3) g"( 4 ) # ($3) $3% = $9.425 ! d " 2x % (9) $ ' at x = 4 dx # f ( x ) & (10) [ f ( x )]2 " 2xf #( x ) 2 [ f ( x )] [ f (4)]2 " 2(4) f #(4) 2 [ f (4)] ! %$( 9(2) " 2( 4 )' * & 2) 2 9 18 " 4$ = 0.067 81 ! ] g"[ f (9)] # f "(9) $ 9$ #9= 2 2 14.137 ! [ g"[ f ( x )] # f "( x ) ! f "( 4 ) # 9 ! d g( f ( x )) at x = 9 dx ! d dx [ ] f (2x ) at x = 2 1 d f (2x )] 2 [ dx "1 1 f 2x [ ( )] 2 # f $(2x ) # 2 2 "1 1 [ f (4)] 2 # f $(4) # 2 2 "1 1 % # (9) 2 # # 2 2 2 % = .524 6

Derivatives by Tables Soilutions

Related Documents

Recommended Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock