Mixed Review For Chapter 3
f'(x) = x^½ - 9 /(20x^(2/5)
#1 Find the derivative.
y' = 5 / (6x^(1/3))
#10 Find the derivative.
y' = (15/4)x^(1/4)
#11 Find the derivative.
y' = 20x⁴ + 1
#12 Find the derivative.
f'(x) = 90x^17
#13 Find the derivative.
f'(x) = 16x³ - 5
#14 Find the derivative.
y' = (-10x⁶ - 8x³ - 60x²) / (2x⁴ - 4)²
#15 Differentiate.
y' = (60x⁶ - 40x⁴ - 44x) / (5x² - 2)²
#16 Differentiate.
y' = (60x⁸ - 48x⁷ - 12x⁵ +100x⁴ + 20x) / (3x⁴ + 5)²
#17 Differentiate.
y' = (9x⁶ - 24x³ - 18x²) / (3x³ - 2)²
#18 Differentiate.
y' = (-32x⁷ + 36x⁶ - 48x² + 24x) / (4x⁵ - 4)²
#19 Differentiate.
f'(s) = 6/(s³) + 16/(s^5)
#2 Find the derivative.
f'(x) = -60x² / (4x³ + 4)²
#20 Differentiate.
f'(x) = -10x⁴ / (x⁵ - 5)²
#21 Differentiate.
f'(x) = 6/(s³) + 16/(s⁵)
#22 Differentiate.
y' = -126x⁸ + 48x⁷ + 210x⁵ - 75x⁴
#23 Differentiate.
y' = 280x⁷ + 105x⁶
#24 Differentiate.
y' = 18x⁵ +95x⁴ - 8x³ + 60x² - 32x
#25 Differentiate.
y' = -280x⁹ - 108x⁸ + 140x - 168x⁵ - 60x⁴ + 60x²
#26 Differentiate.
y' = 18x⁵ - 20x³ + 27x² - 15x
#27 Differentiate.
y' = 8x³ / (-x⁴ - 3)³
#28 Differentiate.
f'(x) = -8x³ / [3(-2x⁴ + 5)^(2/3)]
#29 Differentiate.
y'= -15r⁴ - 10r
#3 Find the derivative.
f'(x) = -2x / (-2x² + 1)^(½)
#30 Differentiate.
f'(x) = -3x³ / (-3x⁴ - 2)^(3/4)
#31 Differentiate.
y' = 40x(5x² + 3)³
#32 Differentiate.
y' = -45x²(-5x³ - 3)²
#33 Differentiate.
y' = -45x⁴(-3x⁵ + 1)²
#34 Differentiate.
y' = 15x²(x³ + 3)⁴
#35 Differentiate.
slope=dy/dx=6x+4
#36 What is the formula for the slope of any line tangent to the curve y=3x²+4x-6?
slope=dy/dx=-2x-3
#37 What is the formula for the slope of any line tangent to the curve y=-x²-3x-6?
slope = dy/dx = 9x²+14
#38 What is the formula for the slope of any line tangent to the curve y=3x³+14x-6?
slope = dy/dx = 15x⁴-12x²
#39 What is the formula for the slope of any line tangent to the curve y=3x⁵-4x³-6?
y' = -2x³ +5x^(2/3) + 2
#4 Find the derivative.
slope = dy/dx = 9x²+14
#40 What is the formula for the slope of any line tangent to the curve y=-2x⁴+4x³-6x?
f"(x) = 120x⁴+24x²+6
#41 Find f"(x) if f(x)= 4x⁶+2x⁴+3x².
f"(x) = 4
#42 Find f"(x) if f(x)=(2x+3)(x-1).
f"(x) = 30x⁴+60x³+36x²-36x-14
#43 Find f"(x) if f(x) = (x²+3x+5)(x⁴-2x²+3).
V(t)= -32t
#44 For position function s(t) = -16t²+100, find the velocity function.
a(t) = -32
#45 For position function s(t) = -16t²+100, find the acceleration function.
-4
#46 Find the average rate of change for f(x) = x²-6x-1 on the interval [-1, 3].
4
#47 Find the average rate of change for f(x) = x²-3 on the interval [1, 3].
4
#48 Find the average rate of change for f(x) = -2x²+6x on the interval [-1, 2].
187
#49 Find the instantaneous rate of change for f(t) = 7t³-2t for t=3.
y' = (8/3)x³ + 5 + 3/(x⁴)
#5 Find the derivative.
-158 ft/sec
#50 For position function s(t) = -16t²+34t+80, find the velocity at 6 seconds.
-68 feet/second
#51 For position function s(t) = -16t²+60t+85, find the velocity at 4 seconds.
-79.28 ft/sec
#52 For position function s(t) = -16t²+34t+80, find the velocity of the object when it hits the ground.
y = 15x-14
#53 Write an equation in slope-intercept form for the line tangent to y = 3x²+3x-2 through the point (2,16).
y = 108x-218
#54 Write an equation in slope-intercept form for the line tangent to y = 4x³-2 through the point (3,106).
y = -13x+16
#55 Write an equation in slope-intercept form for the line tangent to y = -4x²+3x through the point (2,-10).
f'(x) = -1 / (2x^(3/4))
#6 Find the derivative.
y' = 2 / (3x^(1/3))
#7 Find the derivative.
y' = -9 / (x⁴)
#8 Find the derivative.
y' = 20 / (x⁶)
#9 Find the derivative.
