Word Probs
Product Rule
Chain Rule
Logarithmic and Exponential Derivatives
100

A particle moves along the x-axis. The following function v(t) gives the particle's velocity at any time t≥0. 

v(t)= t3-3t2-8t+3. 

What is the particles velocity at t=4.


-13

100

Find the derivative of y = 3x2 (7x+2)

y'=3x2(7)+(7x+2)(6x)

100
Find y' if y = (3x - 9)4
12(3x - 9)3
100

Find the derivative of y = ex. 

y' = ex

200

A plane takes off from an airport at sea level and its altitude (in feet) at time t (in minutes) is given by 

h = 2000 ln (t + 1). Find the rate of climb at time t = 3 min

500 ft/min

200
f(x) = (3x - 2x2)(5 + 4x)
-24x2 + 4x + 15
200

Find the derivative of f(x) = (4x4+5x)9

y'=9(4x4+5x)8(16x3+5)
200
f(x) = ln(x2)
2/x
300

A computer is programmed to inscribe a series of rectangles in the first quadrant under the curve of y= e-x. If area of the rectangle at any point x is given by A=xe-x, what is the area of the largest rectangle that can be inscribed? (Hint: max or min occurs when derivative equals 0).

 0.3679 units2 

300
Find the derivative of y = (5x - 2)/(x2 + 1)
(-5x2 + 4x + 5)/(x2 + 1)2
300
Find y' if y = (9x2 + 4)1/3
(6x)/(9x2 + 4)2/3
300
f(x) = 3x2
f'(x) = 2x ln3 3x2
400

A weight that is attached to the end of a spring is pulled and then released. The function H gives its height, in centimeters, after t seconds. What is the best interpretation for the following statement? 

H'(0)= 3

When the weight is released, its height is increasing at a rate of 3 centimeters per second.

400
Find the derivative of f(x) = (2x + 5)/(x)1/2
(2x - 5)/(2x3/2)
400

f(x) = -2(6x2+3x)3. Find f'(x)

-6(6x2+3x)2(12x+3)

400

f(x) = ln(4x4-9x)

f'(x) =[ 1/(4x4-9x)]*(16x3-9)

500
Let f(x)= e3x. The line L is the range to the curve of f at (0,1). Find the equation of L in the form y=mx+c.

y=3x+1

500

The derivative of 3x(5x3-2x)

What is 3x(15x2-2)+(5x3-2x)(3)

500

The derivative of y=6(9x2+4)7

y'=42(9x2+4)6(18x)

500

y = ln(8x2+3x-5)

y'=(16x+3)/(8x2+3x-5)

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