Quiz about Product and Quotient Rule for Derivatives

Question 1

Find the derivative of y = 2x² (3x - 4)

Accepted Answer

18x² - 16x

Answer

6x³ - 8x²

Answer

15x2 - 6x

Answer

6x - 4

Question 2

Which if the following is not a correct notation for 'derivative?'

Accepted Answer

dy

Answer

f'(x)

Answer

y'

Answer

dy/dx

Question 3

Derivative means the same thing as

Accepted Answer

slope of the tangent line

Answer

slope of the normal line

Answer

exponent

Answer

slope of the secant line

Question 4

Given that the position function for a particular object is given by
s(t) = t³- 3t +5, find the velocity of the object at t = 2 seconds.

Accepted Answer

9

Answer

51

Answer

12

Answer

6

Question 5

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

Accepted Answer

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

Answer

9x²+2 $$9x^2+2$$

Answer

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

Answer

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

Answer

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

Question 6

What is the derivative of e^x?

Accepted Answer

ex

Answer

xex-1

Answer

xe

Answer

ex-1

Question 7

Is differentiating the same as taking the derivative?

Accepted Answer

yes

Answer

no

Answer

sometimes

Question 8

Find the derivative of the given equation $$x^3+x^2+12$$

Accepted Answer

$$3x^2+2x$$

Answer

$$5x$$

Answer

$$3x^3+2x^2$$

Answer

$$x^2+x$$

Question 9

Question 9.

Accepted Answer

$$\frac{\left(8x^4-60x^2\right)}{\left(2x^2-5\right)^2}$$

Answer

$$8x^4-60x^2$$

Answer

16x4

Answer

$$2-\frac{12}{5}x^2$$

Question 10

Find the first step of the derivative of y = 2x² (3x - 4) using the product rule.

Accepted Answer

2x² (3) + (3x - 4)(4x)

Answer

6x³ - 8x²

Answer

(3x)(2x²)+ (4x² )(3x - 4)

Answer

4x2 (3)

Question 11

$$If\ y=\frac{3}{4+x^2},\ then\ \frac{dy}{dx}=$$

Accepted Answer

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

Answer

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

Answer

$$\frac{3x}{\left(1+x^2\right)^2}$$

Answer

$$\frac{6x}{\left(4+x^2\right)^2}$$

Answer

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

Question 12

Given that $$y=\frac{x+2}{x-3}$$

Find y'

Accepted Answer

$$y$$

Answer

$$y$$

Question 13

Let f(x) = (x - 1)(x + 2). Find f'(0)

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 14

How many derivatives can you take of a function?

Accepted Answer

until you can no longer derive it

Answer

only 3

Answer

only 2

Answer

only 1

Question 15

Find the derivative of g(x)=(3x-2)/(x²+2)

Accepted Answer

(-3x²+4x +6)/(x²+2)²

Answer

9x2+2

Answer

3(x²+2)/(x²+2)²

Answer

(-3x²+10)/(x²+2)²

Question 16

Find the derivative.
y = x²/ (3x-1)

Accepted Answer

y' = (3x² - 2x) / (3x-1)²

Answer

y' = 9x²- 12
y' = (3x-1) / (3x-1)²

Answer

y' = (6x+1)²/ 3

Question 17

Find the derivative of y = 2x² (3x - 4)

Accepted Answer

18x² - 16x

Answer

6x³ - 8x²

Answer

15x2 - 6x

Answer

6x - 4

Question 18

Find the derivative of f(x) = x²sinx

Accepted Answer

f'(x) = 2xsinx + x²cosx

Answer

f'(x) = 2xsinx - x²cosx

Answer

f'(x) = 2xsinx + x²sinx

Answer

f'(x) = 2xcosx

Question 19

Question 19.

Accepted Answer

sec2x

Answer

cscx cotx

Answer

secx tanx

Answer

-cscx cotx

Question 20

Let g(x) = (2x + 3)(x - 4). Find g'(1).

Accepted Answer

-1

Answer

-2

Answer

1

Answer

6

Product and Quotient Rule for Derivatives

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