Free Printable basic cal

1.

This rule states that the derivative of a constant function is zero; that is, since a constant function is a horizontal line, the slope, or the rate of change, of a constant function is 0.

a)

The Power Rule

b)

The Constant Rule

c)

The Sum, Difference, and Constant Multiple Rules

d)

The Product Rule

2.

This rule is used to differentiate functions of the form f(x) = x^r, whenever r is a real number.

a)

The Sum, Difference, and Constant Multiple Rules

b)

The Product Rule

c)

The Quotient Rule

d)

The Power Rule

3.

The derivative of the sum of a function f and a function g is the same as the sum of the derivative of f and the derivative of g.

a)

Sum Rule

b)

Difference Rule

c)

Constant Multiple Rule

d)

The Sum, Difference, and Constant Multiple Rules

4.

The derivative of a constant k multiplied by a function f is the same as the constant multiplied by the derivative.

a)

Constant Multiple Rule

b)

The Sum, Difference, and Constant Multiple Rules

c)

Difference Rule

d)

Sum Rule

5.

The derivative of the difference of a function f and a function g is the same as the difference of the derivative of f and the derivative of g.

a)

Sum Rule

b)

The Sum, Difference, and Constant Multiple Rules

c)

Difference Rule

d)

Constant Multiple Rule

6.

This rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

a)

The Product Rule

b)

Constant Multiple Rule

c)

The Power Rule

d)

The Constant Rule

7.

This rule states that the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

a)

The Sum, Difference, and Constant Multiple Rules

b)

The Power Rule

c)

Constant Multiple Rule

d)

The Quotient Rule

8.

The derivative of a constant is

a)

two

b)

five

c)

one

d)

zero

9.

Find the derivative of the following:

y= -2

a)

2x+2

b)

0

c)

3.7x^2.5

d)

9x⁸- 40x⁷+ 1

10.

Determine the name of the given rule:

If $f\left(x\right)=c$ , then $f'\left(x\right)=0$ .

a)

Derivative of a Constant

b)

Power Rule

c)

Derivative of the Product of a Constant and a Function

d)

Sum and Difference Rule

11.

Determine the name of the given rule:

If $f\left(x\right)=x^n$ , then $f'\left(x\right)=nx^{n-1}$ .

a)

Derivative of a Constant

b)

Power Rule

c)

Derivative of the Product of a Constant and a Function

d)

Sum and Difference Rule

12.

Determine the name of the given rule:

If $h\left(x\right)=f\left(x\right)\pm g\left(x\right)$ , then $h'\left(x\right)=f'\left(x\right)\pm g'\left(x\right)$ .

a)

Derivative of a Constant

b)

Power Rule

c)

Derivative of the Product of a Constant and a Function

d)

Sum and Difference Rule

13.

Simplify:

$\frac{d}{dx}\left(x^{18}\right)=$

a)

$18x^{17}$

b)

$x^{18}$

c)

$17x^{18}$

d)

None of These

14.

Simplify:

$\frac{d}{dx}\left(x^5-x^3\right)$

a)

$5x^4-3x^2$

b)

$x^5-x^3$

c)

$4x^5-2x^3$

d)

None of These

15.

Given $f\left(x\right)=3x^2+2x-1$ , which of the following is the correct derivative?

a)

$f'\left(x\right)=6x^2+2$

b)

$f'\left(x\right)=6x+2$

c)

$f'\left(x\right)=6x^2+2$

d)

$f'\left(x\right)=6x^2+2x^2-x$

16.

Find the derivative for $f\left(x\right)=\sqrt{1-2x^2}$

a)

$f'\left(x\right)=\frac{-2x}{\sqrt{1-2x^2}}$

b)

$f'\left(x\right)=\frac{2x}{\sqrt{1-2x^2}}$

c)

$f'\left(x\right)=-2x\sqrt{1-2x^2}$

d)

$f'\left(x\right)=\frac{-4x^2}{\sqrt{1-2x^2}}$

17.

Given $f\left(x\right)=3x^2+2x-1$ , which of the following is the correct derivative?

a)

$f'\left(x\right)=6x^2+2$

b)

$f'\left(x\right)=6x+2$

c)

$f'\left(x\right)=6x^2+2$

d)

$f'\left(x\right)=6x^2+2x^2-x$

18.

Which of the following is the correct definition of the Power Rule of derivatives?

a)

Given $f\left(x\right)=x^n$ , $f'\left(x\right)=x^{n-1}$

b)

Given $null$ , $f'\left(x\right)=nx^{n-1}$

c)

Given $null$ , $f'\left(x\right)=\frac{x^{n-1}}{n}$

d)

Given $null$ , $f'\left(x\right)=\frac{n}{x^{n-1}}$

19.

What is the derivative of 0?

a)

You can't take the derivative of 0.

b)

0

c)

This is all derivative.

d)

Any constant

20.

What is the derivative of f(x)= 1,000,000

a)

0

b)

1

c)

-1

d)

1,000,000

21.

$\frac{\text{d}}{\text{d}y}\left(\sin x\right)$

a)

$\cos x$

b)

$-\cos x$

c)

$\sin^{-1}x$

d)

$\frac{1}{\sin x}$

e)

$\sin x\cos x$

22.

$\frac{\text{d}}{\text{d}y}\left(\tan x\right)$

a)

$\sec^2x$

b)

$-\sec^2x$

c)

$\tan^{-1}x$

d)

$\frac{1}{\tan x}$

e)

$\sec x$

23.

$\frac{\text{d}}{\text{d}y}\left(\csc x\right)$

a)

$-\csc x\cot x$

b)

$\csc x\cot x$

c)

$\csc^{-1}x\cot^{-1}x$

d)

$\frac{1}{\csc x\cot x}$

e)

$-\sec x\tan x$

24.

$\frac{\text{d}}{\text{d}y}\left(2\sin x+x^3\right)$

a)

$2\cos x+3x^2$

b)

$-2\cos x+3x^2$

c)

$2\cos x+4x^4$

d)

$2\cos x+2x^2$

e)

$-2\cos x+2x^2$

25.

$\frac{\text{d}}{\text{d}y}\left(3\tan^4x\right)$

a)

$12\tan^3x\sec^2x$

b)

$12\tan^3x\sec x$

c)

$12\sec^3x$

d)

$12\sec^6x$

e)

$12\sec^2x$

26.

$\frac{\text{d}}{\text{d}y}\left(2\cos^3\left(2x\right)-2\right)$

a)

$-12\cos^2\left(2x\right)\sin\left(2x\right)$

b)

$-6\cos^2\left(2x\right)\sin\left(2x\right)$

c)

$-12\sin^2\left(2x\right)$

d)

$-6\sin^2\left(2x\right)$

e)

$-2\sin^2\left(2x\right)$

27.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\cos\left(4x\right)

is

a)

-2 sin (4x)

b)

2 sin (4x)

c)

-8 sin (4x)

d)

8 sin (4x)

28.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\sin\left(4x\right)

is

a)

8 cos (4x)

b)

-8 cos (4x)

c)

2 cos (4x)

d)

- 2 cos (4x)

29.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\sec\left(4x\right)

is

a)

$-2\ \sec\left(4x\right)\tan\left(4x\right)$

b)

$8\ \sec\left(4x\right)\tan\left(4x\right)$

c)

$2\ \sec\left(4x\right)\tan\left(4x\right)$

d)

$-8\ \sec\left(4x\right)\tan\left(4x\right)$

30.

Given $f\left(x\right)=\tan^3\left(4x^2\right)$ . The derivative, $f'\left(x\right)$

is

a)

$3\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

b)

$12\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

c)

$24\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

d)

$24x\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

31.

Given $f\left(x\right)=\cos^5\left(2x^3\right)$ . The derivative, $f'\left(x\right)$

is

a)

$-30x^2\cos^4\left(2x^3\right)\sin\left(2x^3\right)$

b)

$-5x^2\cos^4\left(2x^3\right)\sin\left(2x^3\right)$

c)

$5x^2\cos^4\left(2x^3\right)\sin\left(2x^3\right)$

d)

$30x^2\cos^4\left(2x^3\right)\sin\left(2x^3\right)$

32.

Which of the following is the absolute maximum value of the function y = x³ –3x² -1 on the given interval [-1, 4]?

a)

-1

b)

5

c)

15

d)

49

33.

Find the absolute extrema of

g(x) = 3x³ + 6x² on [-1, 1].

a)

abs max value of $\frac{32}{9}$ when x = $-\frac{4}{3}$ abs min value of 0 when x = 0

b)

abs max value of 9 when x = 1, abs min value of 3 when x = -1

c)

abs max value of 9 when x = 1, abs min value of 0 when x = 0

d)

abs max value of 9 when x = 1, abs min of -1 when x = -1

34.

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

35.

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

basic cal

Total questions: 35

Worksheet time: 1hrs 15mins

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