Free Printable DERIVE

1.

What main rule should be applied to this problem?
$\tan\left(4x-2\right)$

a)

Chain rule

b)

Product rule

c)

Quotient rule

d)

Power Rule

2.

Based on the image, where is the slope 0?

a)

x = -1

b)

x = 2

c)

x = 0

d)

x = 1

3.

What is the derivative for $\sqrt{4x-3x^2}$

a)

$\frac{\sqrt{4x-3x^2}}{2\left(4x-3x^2\right)}$

b)

$\frac{\sqrt{4x-3x^2}\left(4-6x\right)}{2\left(4x-3x^2\right)}$

c)

$\sqrt{4x-3x^2}\left(4-6x\right)$

d)

$\frac{\sqrt{4x-3x^2}}{4-6x}$

4.

Derive $f\left(x\right)\ =\ 3x^3+4x^2+3$ with respect to x.

a)

$9x^2+8x$

b)

$9x^2+8x+3$

c)

No derivative

d)

$3x^2+4x$

5.

What is the derivative of $3x-4t-3x^2+6t^2$ with respect to t?

a)

$-4+12t$

b)

$3-6x$

c)

$-4t\ +6t^2$

d)

0

6.

What kind of function would the derivative of the image be?

a)

Cubic

b)

Linear

c)

Quadratic

d)

Horizontal line

7.

Based on the image, what kind of function would it's derivative be?

a)

Quadratic

b)

Linear

c)

Cubic

d)

Horizontal

8.

Derive $\cos\left(3x+5\right)$ with respect to t.

a)

$-3\sin\left(3x+5\right)$

b)

$3\sin\left(3x+5\right)$

c)

0

d)

$-3\cos\left(3x+5\right)$

9.

Derive $\cos\left(3x+5\right)$ with respect to x

a)

$-\sin\left(3x+5\right)$

b)

$-3\sin\left(3x+5\right)$

c)

$-3\cos\left(3x+5\right)$

d)

$3\sin\left(3x+5\right)$

10.

Derive $e^{\left(5x+1\right)}$ with respect to x

a)

$e^{5x}$

b)

$5e^{5x}+1$

c)

$5e^{\left(5x+1\right)}$

d)

$5e^x$

11.

$\frac{d}{dx}4x+5$

a)

0

b)

4

c)

5

d)

4x+5

12.

The average velocity of a function can be represented by finding the ....

a)

Instantaneous rate of change of that function

b)

Difference quotient of the function

c)

Graphing the function

d)

Measuring the time of the function

13.

The slope of a tangent line of a curve at a point can be found by....

a)

Finding the average rate of change of the curve

b)

Applying the difference quotient to the curve

c)

Finding the derivative of the curve at that point

d)

Determining where the slope is equal to 1

14.

$\frac{\left(3x+5\right)}{2x^2+5}$

What main rule would be applied to the equation above?

a)

Chain

b)

Product

c)

Quotient

d)

Power

15.

$\frac{d}{dx}\ \frac{e^x}{x}$

a)

$\frac{e^x}{x}-e^x$

b)

$\frac{e^x}{x}-\frac{e^x}{x^2}$

c)

$\frac{\left(xe^x-e^x\right)}{x^2}$

d)

$e^x$

16.

$\frac{d}{dx}\ \cos\left(\sin\left(3x\right)\right)$

a)

$-\sin\left(\sin\left(3x\right)\cos\left(3x\right)\right)$

b)

$3\sin\left(\sin\left(3x\right)\right)\cos\left(3x\right)$

c)

$\cos\left(\sin\left(3x\right)\right)\cos\left(3x\right)$

d)

$-3\sin\left(\sin\left(3x\right)\right)\cos\left(3x\right)$

17.

$f\left(x\right)\ =\ 3x^2+3x$

What is the rate of change at the point x = 4 for the function above?

a)

18

b)

27

c)

21

d)

30

18.

What was the function if the derivative was the graph above?

a)

linear

b)

quadratic

c)

cubic

d)

quartic

19.

\frac{d}{dx}\sin\left(x^2\right)

a)

$2\cos\left(x^2\right)$

b)

$2x\cos\left(2x\right)$

c)

$2x\cos\left(x^2\right)$

d)

$2x\cos\left(x\right)$

20.

How many slopes of zero does the function

$f\left(x\right)\ =\ 3x^2+3x+1$ have?

a)

1

b)

2

c)

3

d)

0

DERIVE

Total questions: 20

Worksheet time: 12mins

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