−5x3+45x2−90x Answer Key

Calculus ZH X Name eo U ye sY q Dt Z T AZ E PR_ v ________________________________ ID: 1 S Product, Quotient Rule, Higher Order Date________________ Period____ Differentiate each function with respect to x. 1) y = 2) y = ( x 5 + 4) × 5x 4 3x 5 - 2x 4 x2 - 3 dy ( x - 3)(15x - 8x ) - (3x - 2x = dx ( x 2 - 3) 2 9x 6 - 4x 5 - 45x 4 + 24x 3 = x 4 - 6x 2 + 9 2 4 3 5 4 ) × 2x 3) y = (2x 4 + 2)(2x 4 + 5) dy = (2x 4 + 2) × 8x 3 + (2x 4 + 5) × 8x 3 dx = 32x 7 + 56x 3 dy = ( x 5 + 4) × 20x 3 + 5x 4 × 5x 4 dx = 45x 8 + 80x 3 ( 4) y = 4x + 3 (4x 3 + 2) ( -4 )(2x 3 - 1) dy -4 -5 = (2 + 5x ) × 6x 2 + (2x 3 - 1) × -20x dx 10 20 = 12x 2 - 2 + 5 x x ) 4 1 dy 16 3 3 = 4x + 3 × 12x 2 + (4x 3 + 2) × x dx 3 = 5) y = (2 + 5x ) 4 3 208x 3 10 3 + 36x 2 + 32x 3 1 3 6) y = (5x 5 + 3)(4x 2 + 2) dy = (5x 5 + 3) × 8x + (4x 2 + 2) × 25x 4 dx = 140x 6 + 50x 4 + 24x Worksheet by Kuta Software LLC 7) y = 4x 5 + 5 x4 + 4 8) y = dy ( x 4 + 4) × 20x 4 - (4x 5 + 5) × 4x 3 = dx ( x 4 + 4) 2 4x 8 + 80x 4 - 20x 3 = x 8 + 8x 4 + 16 1 4x - 4 2 dy 8x =dx (4x 2 - 4) 2 x =- 4 2x - 4x 2 + 2 9) y = (-4x 4 + 4)( x 3 + 4) ( ) 4 3 10) y = 3x + 5 ( x 3 - 1) dy = (-4x 4 + 4) × 3x 2 + ( x 3 + 4) × -16x 3 dx = -28x 6 - 64x 3 + 12x 2 ( = 13x 11) y = 5 1 2 + 15x - 4x -3 1 3 )( x 4 + 5) 2 x +5 4 ( 2x + 5)(15x - 8x) - (5x - 4x ) × x dy 5 = dx (2x + 5) 2 5 2 3 2 2 5 = 10 3 12) y = (5 + 3x 5x 3 - 4x 2 2 ) 4 dy 3 3 = 3x + 5 × 3x 2 + ( x 3 - 1) × 4x dx 130x 12 5 2 3 5 dy -3 -4 = (5 + 3x ) × 4x 3 + ( x 4 + 5) × -9x dx 45 = 20x 3 + 3 - 4 x 7 5 2 + 375x - 64x - 200x 4 5 2 5 20x + 100x + 125 Worksheet by Kuta Software LLC ( ) 13) y = 5 + 4 (-2x 3 + 4) 2 x dy -2 -3 = (5 + 4x ) × -6x 2 + (-2x 3 + 4) × -8x dx 32 = -30x 2 - 8 - 3 x 15) y = 3 3 5x + 4 dy 3 × 15x 2 =dx (5x 3 + 4) 2 45x 2 =25x 6 + 40x 3 + 16 14) y = (2x 4 + 3) × 4x 5 dy = (2x 4 + 3) × 20x 4 + 4x 5 × 8x 3 dx = 72x 8 + 60x 4 16) y = 4x 2 - 4 4 5 5x + 5 ( ) 4 5 - dy 5x + 5 × 8x - (4x - 4) × 4x = 2 4 dx 5 5x + 5 2 ( 1 5 ) 6 5 24x 2 + 40x + 16 = 9 5 25x + 50x + 25x 17) y = (3x 4 + 1) × -3x 3 18) y = 1 5 5x 5 + 3x 2 4 3 dy = (3x 4 + 1) × -9x 2 - 3x 3 × 12x 3 dx = -63x 6 - 9x 2 x +5 ( dy = dx = )( 4 3 1 4 3 x + 5 25x + 6x) - (5x + 3x ) × x 3 4 5 ( 55x 16 3 4 3 x +5 ) 2 2 7 3 + 375x 4 + 6x + 90x 8 3 4 3 3x + 30x + 75 Worksheet by Kuta Software LLC 19) y = (3x 4 + 5)(5x 2 + 3) 20) y = dy = (3x 4 + 5) × 10x + (5x 2 + 3) × 12x 3 dx = 90x 5 + 36x 3 + 50x 5x 4 - 3x 2 3 ( dy = dx = 2 x +2 2 ) 2 3 1 4 -3 2x + 2 (20x - 6x) - (5x - 3x ) × x 3 3 4 (2x + 2) 2 3 25x 11 3 2 2 5 3 3 + 30x - 6x - 9x 4 3 2 3 3x + 6x + 3 21) y = 22) y = -5x 5 (-5x 3 - 4) x 4 + 2x 3 3x 2 + 2 dy (3x + 2)(4x + 6x ) - ( x + 2x = dx (3x 2 + 2) 2 5 4 6x + 6x + 8x 3 + 12x 2 = 9x 4 + 12x 2 + 4 2 23) y = 3 2 4 3 ) × 6x 24) y = 5x 5 ( x 5 + 3) 3x 4 + 5x 2 5 - 3x -2 dy (5 - 3x = dx = dy = -5x 5 × -15x 2 + (-5x 3 - 4) × -25x 4 dx = 200x 7 + 100x 4 -2 )(12x 3 + 10x) - (3x 4 + 5x 2 ) × 6x -3 (5 - 3x -2) 2 dy = 5x 5 × 5x 4 + ( x 5 + 3) × 25x 4 dx = 50x 9 + 75x 4 60x 7 - 4x 5 - 60x 3 25x 4 - 30x 2 + 9 Worksheet by Kuta Software LLC 25) y = 5x 3 5x 4 + 3 26) y = dy (5x 4 + 3) × 15x 2 - 5x 3 × 20x 3 = dx (5x 4 + 3) 2 -25x 6 + 45x 2 = 25x 8 + 30x 4 + 9 dy (2x - 5) × 15x - (5x + 3) × 4x = dx (2x 2 - 5) 2 10x 4 - 75x 2 - 12x = 4x 4 - 20x 2 + 25 29) y = dy (3x 5 + 3) × 25x 4 - 5x 5 × 15x 4 = dx (3x 5 + 3) 2 25x 4 = 10 3x + 6x 5 + 3 28) y = (-3x 2 - 1)(-2x 2 + 3) 5x 3 + 3 27) y = 2 2x - 5 2 5x 5 3x 5 + 3 2 3 5 x +2 dy 3 × 5x 4 =dx ( x 5 + 2) 2 15x 4 = - 10 x + 4x 5 + 4 3 dy = (-3x 2 - 1) × -4x + (-2x 2 + 3) × -6x dx = 24x 3 - 14x 30) y = 3x 5 + 3x 2 4x 3 + 5 dy (4x 3 + 5)(15x 4 + 6x) - (3x 5 + 3x 2 ) × 12x 2 = dx (4x 3 + 5) 2 7 4 24x + 63x + 30x = 16x 6 + 40x 3 + 25 Worksheet by Kuta Software LLC For each problem, find the indicated derivative with respect to x. 31) f ( x) = x 5 32) f ( x) = 2x 4 + 5x Find f '' f '' ( x) = 20x 3 f ''' ( x) = 48x 33) f ( x) = -5x 3 + 4x 2 + 5x f ( 4) Find f ( x) = 0 35) f ( x) = -3x 5 - 3x f ''' ( x) = -180x 2 Find f ''' (4) 34) f ( x) = 4x 5 + 2x 4 - 3x f Find f ''' Find f ( 4) (4 ) ( x) = 480x + 48 36) f ( x) = -x 4 Find f '' f '' ( x) = -12x 2 Worksheet by Kuta Software LLC 37) f ( x) = -4x 5 + 2x 3 38) f ( x) = 5x 3 + 4x 2 + 3x Find f ''' f ''' ( x) = -240x 2 + 12 39) f ( x) = x 5 + 4x 2 + 5x f ( 4) f Find f ( 4) 42) f ( x) = -x Find f '' Find f ''' Find f '' f '' ( x) = 0 43) f ( x) = -x 5 + 5x 3 - x 2 ( 4) ( x) = 0 f ''' ( x) = 12 f '' ( x) = 24x f ( 4) (4 ) 40) f ( x) = 2x 3 + 5x ( x) = 120x 41) f ( x) = 4x 3 Find f Find f (4) 44) f ( x) = -x 4 + 5x 2 + 2x ( x) = -120x f Find f (4) (4 ) ( x) = -24 Worksheet by Kuta Software LLC Q _ j Q g j q y 45) f ( x) = 4x 5 + 5x 3 + 5x f ( 4) ( 4) ( 4) ( x) = 600x - 96 46) f ( x) = -5x 5 + 3x 3 + 4x 2 f Find f (4) Find f ( 4) (4 ) ( x) = -600x 48) f ( x) = -4x 5 + x 4 Find f ''' f ''' ( x) = -240x 2 + 24x ( x) = 96 49) f ( x) = 5x 5 - 4x 4 + x 2 f (4) ( x) = 480x 47) f ( x) = 4x 4 + 2x 3 + 5x 2 f Find f Find f (4) 50) f ( x) = 5x 5 Find f '' f '' ( x) = 100x 3 W rksheet by Kuta Software LLC