Free Printable Unit 3 Review

1.

What rule should be used in deriving h(x) = 2(x - 4)³

a)

Power rule

b)

Product rule

c)

Quotient rule

d)

Chain rule

2.

Find the derivative of
f(x) = (x⁶ + 4)⁵

a)

f '(x) = 5x⁵(x⁴ + 4)⁴

b)

f '(x) = 6x⁵(x⁶ + 4)⁴

c)

f '(x) = 30x⁵(x⁶ + 4)⁴

d)

f '(x) = 30x⁶(x⁶ + 4)⁴

3.

Differentiate f(x) = (9 - 4x²)^-1

a)

8x/(9 - 4x²)^-2

b)

8x/(9 - 4x²)²

c)

-8x/(9 - 4x²)^-2

d)

-8x(9 - 4x²)²

4.

When do you use the chain rule?

a)

anytime you want

b)

when there is a function in a function

c)

where there are multiple layers to a lasagna (yum)

d)

when there is division

5.

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

a)

y = 500x + 400

b)

y = 100x + 400

c)

y = -500 x - 400

d)

y = 500x - 400

6.

a)

A

b)

B

c)

C

d)

D

7.

find y' for y=(e^5x)+1

a)

5e^5x+1

b)

e^5x

c)

5e^5x

d)

1

8.

find y' for y= sin(2x²)

a)

4sin(2x²)

b)

4xcos(2x²)

c)

2xcos(2x²)

d)

xcos(4x²)

9.

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

a)

6 -x

b)

3x² +3y²

c)

−x²/y²

d)

0

10.

Find dy/dx by Implicit Differentiation
xy = 6

a)

-x/ y

b)

-y/ x

c)

-6y/ x

d)

y/x

11.

Find dy/dx at a given point.

a)

5/4

b)

4/5

c)

1

d)

-5

12.

Find dy/dx for
y = (x² + 1)³

a)

dy/dx = 3(x² + 1)²

b)

dy/dx = 3(2x)²

c)

dy/dx = 6x(x² + 1)²

d)

dy/dx = 2x(x² + 1)²

13.

Find dy/dx
xy+y²=2

a)

-y/(x+2y)

b)

y/(x+2y)

c)

-3y/x

d)

-3x/y

14.

Find the second derivative of f(x) = x²+ e^x - cosx

a)

f"(x) = 2 + e^x + cosx

b)

f"(x) = 2x + e^x + cosx

c)

f"(x) = 2x + xe^x - cosx

d)

f"(x) = 2x + e^x + sinx

15.

Which of the following equations, if any, are written in implicit form?

(Check all that apply)

a)

$y=4\ x-9$

b)

$x^{\ 2}+y^{\ 2}=49$

c)

$x\ y=16$

d)

$y=\sqrt{36-x^{\ 2}}$

e)

$y=\frac{25\ x}{x^{\ 2}-64}$

16.

Find f "'(x) when

f(x)=10x⁵ +3x⁴ -5x³ +2x² -10x+6

a)

200x³+36x²-30x+4

b)

600x² +72x -26

c)

600x² +72x -30

d)

600x² +72x -36

17.

Find the second derivative of the following functions with respect to x.
y=(x³+x)/x²

a)

x+(1/x)

b)

1-(1/x²)

c)

2/x²

d)

2/x³

18.

Find the 3rd derivative if

y=3x^4-12x^3+11x^2-8x+10

a)

$\frac{d^3y}{dx^3}=36x^2-72x+22$

b)

$\frac{d^3y}{dx^3}=12x^3-36x^2+22x-8$

c)

$\frac{d^3y}{dx^3}=72x\ -\ 72$

d)

$\frac{d^3y}{dx^3}=72$

e)

$\frac{d^3y}{dx^3}=0$

Unit 3 Review

Total questions: 18

Worksheet time: 36mins

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