Free Printable Calculus Basic rules

1.

Find the derivative:

$f(x)=(-\frac{2}{3})x^3-(\frac{1}{2})x^2+9x$

a)

-2x² - x + 9

b)

-2x² + x + 9

c)

2x² - x + 9

d)

2x² - x - 9

2.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

3.

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

a)

(12x³)*(10x)

b)

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

c)

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

d)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

4.

Differentiate $f(x)=\frac{2}{x^5}-5.$

a)

x⁵- 3

b)

-10 x⁶

c)

x⁵- 5

d)

-10 x^-6

5.

Find the derivative of $g(x)=\frac{(3x-2)}{(x^2+2)}\$ .

a)

9x²+2

b)

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

c)

$\frac{-3x^2+4x+6}{(x^2+2)^2}$

d)

$\ \frac{-3x^2+10}{(x^2+2)^2}$

6.

Find the derivative.
f(x) = -8x^-3 + 5x

a)

f'(x) = -24x^-4 + 5

b)

f'(x) = 24x^-4 + 5

c)

f'(x) = 24x^-2 + 5

d)

f'(x) = 24x^-4 - 5

7.

Find the derivative
f(t) = (t² + 2t)⁵

a)

f'(t) = 5(2t+2)⁴

b)

f'(t) = 5(t² + 2t)⁴

c)

f'(t) = 5(t² + 2t)⁴(2t)

d)

f'(t) = 5(t² + 2t)⁴(2t + 2)

8.

$f(x)=\ \frac{9}{\sqrt[3]{x}}$
f'(x) =

a)

9x^-1/3

b)

-3x^-4/3

c)

-9x^2/3

d)

-3x^2/3

9.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

10.

If f ' (x) = 0 what does that imply about the x value?

a)

It is a critical point, it is a possible max, min, or point of inflection.

b)

That the limit does not exist.

11.

Rate of change is another way of saying..................................

(Choose all the answers that implied.)

a)

The gradient

b)

The slope

c)

dy/dx

12.

The following talks about calculus EXCEPT ONE, what is it?

a)

Area of a Region Bounded by Curves

b)

Length of a Segment

c)

Instantaneous Velocity

d)

Slope of a Curve

13.

What does calculus mean in the field of dentistry?

a)

pebble

b)

beads

c)

tartar

d)

stone

14.

What is the derivative of $f(x)=\pi$ ?

a)

$0$

b)

$1$

c)

$x$

d)

$\pi$

15.

What is the derivative of $f(x)=\frac{2}{3}x$ ?

a)

$0$

b)

$\frac{2}{3}$

c)

$-\frac{3}{2}$

d)

$\frac{3}{2}$

16.

What is the derivative of $f(x)=x^{20}$ ?

a)

$20x$

b)

$19x$

c)

$20x^{19}$

d)

$19x^{20}$

17.

What is the derivative of $f(x)=x^{-3}$ ?

a)

$-3x^2$

b)

$-3x^4$

c)

$-\frac{3}{x^2}$

d)

$-\frac{3}{x^4}$

18.

What is the derivative of $f(x)=3x^{\frac{1}{2}}$ ?

a)

$\frac{3}{2\ \sqrt[]{x}}$

b)

$\frac{2}{3\ \sqrt[]{x}}$

c)

$-\frac{3}{2\ \sqrt[]{x}}$

d)

$-\frac{2}{3\ \sqrt[]{x}}$

19.

What is the equation of the normal line of $f(x)=3x^2+5$ at a point $(1,8)$ ?

a)

$6y\ -\ x\ =49$

b)

$y=\frac{1}{6}x\ +49$

c)

$y=\frac{1}{6}x\ +\frac{49}{6}$

d)

$6y+x=49$

20.

What is the equation of the line tangent to $f(x)=3x^2+5$ at a point $(1,8)$ ?

a)

$y=-14x+25$

b)

$y=6x+2$

c)

$y=-14x+31$

d)

$y=6x-14$

Calculus Basic rules

Total questions: 20

Worksheet time: 40mins

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