Quiz about Y11 - Derivative Revision

Question 1

Find the derivative of f(x) = 2x²+3.

Accepted Answer

4x

Answer

4x2

Answer

3

Answer

4x+3

Question 2

Find the derivative of the given equation
f(x) = x³ + x² + 3

Accepted Answer

3x2 + 2x

Answer

3x + 2x

Answer

3x + 2x + 3

Answer

x3 + x2

Question 3

Differentiate y= 12x^-2

Accepted Answer

-24x-3

Answer

24x-1

Answer

-24x-1

Answer

6x-3

Question 4

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

Accepted Answer

0

Answer

7

Answer

7x

Answer

14

Question 5

Differentiate with respect to x...

Accepted Answer

x2 + x

Answer

x2 - x

Answer

x2 + x3

Answer

x2 - x-3

Question 6

What is the equation of the line tangent to the curve y = x² at x = 1?

Accepted Answer

y = 2x - 1

Answer

y = 2x + 1

Answer

y = -2x + 1

Answer

y = x - 1

Question 7

What is the equation of the line tangent to the curve y = -x² + 3 at (1, 2)?

Accepted Answer

y = -2x + 4

Answer

y = 2x - 4

Answer

y = -2x - 4

Answer

y = 2x + 4

Question 8

Find the slope at x = 3 of the equation f(x) = 3x²

Accepted Answer

18

Answer

6x

Answer

27

Answer

3x

Question 9

What is the slope of the line normal to the curve y = x² + x at x = 1?

Accepted Answer

-1/3

Answer

-1

Answer

-1/2

Answer

-1/4

Question 10

When we "take the derivative" of a function what are we finding?

Accepted Answer

The slope of the tangent line

Answer

What's a derivative?

Answer

The rate at which our struggles in Calculus are increasing.

Answer

The slope of the secant line

Question 11

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

Accepted Answer

f '(x) = 5(x⁶ + 4)⁴ $$\cdot$$ 6x⁵

Answer

f '(x) = 5(x⁴ + 4)⁴ $$\cdot$$ x⁵

Answer

f '(x) = 6(x⁶ + 4)⁴ $$\cdot$$ x⁵

Answer

f '(x) = 5(x⁶ + 4)⁴ $$\cdot$$ 6x⁶

Question 12

find y' for y= sin(2x²)

Accepted Answer

cos(2x²) $$\cdot\ 4x$$

Answer

sin(2x²) $$\cdot\ 4$$

Answer

cos(2x²) $$\cdot\ 2x$$

Answer

cos(4x²) $$\cdot\ x$$

Question 13

Find $$\frac{dr}{d heta}\ if\ r=\left(\sec heta+ an heta ight)^{-3}$$

Accepted Answer

$$-3\left(\sec heta+ an heta ight)^{-4}\left(\sec heta an heta+\sec^2 heta ight)$$

Answer

$$-3\left(\sec heta+ an heta ight)^{-4}\cdot\sec heta$$

Answer

$$-3\left(\sec heta+ an heta ight)^{-4}$$

Answer

$$-3\left(\sec heta an heta+\sec^2 heta ight)^{-4}$$

Question 14

Find $$\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}$$

Accepted Answer

$$-\sin\sqrt{10t+12}\cdot\frac{1}{2}\left(10t+12\right)^{-\frac{1}{2}}\cdot10$$

Answer

$$-\sin\sqrt{10t+12}\cdot\frac{1}{2}\left(10t+12\right)^{-\frac{1}{2}}$$

Answer

$$-\sin\sqrt{10t+12}$$

Answer

$$-\sin\left(\frac{1}{2}\left(10t+12\right)^{-\frac{1}{2}}\cdot10\right)$$

Question 15

When do you use the chain rule?

Accepted Answer

when there is a function in a function

Answer

when there is multiplication

Answer

when there is division

Question 16

Differentiate (sin x)²

Accepted Answer

2(sin x)(cos x)

Answer

(cos x)2

Answer

2(cos x)

Answer

-2(sin x)(cos x)

Question 17

$$\frac{ ext{d}}{ ext{d}x} an^2\left(3x ight)$$

Accepted Answer

$$2 an\left(3x ight)\sec^2\left(3x ight)\cdot3$$

Answer

$$2 an\left(3x ight)\sec^2\left(x ight)\cdot3$$

Answer

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

Answer

$$2\sec^2\left(3x\right)\cdot3$$

Question 18

$$find\ g$$

Accepted Answer

$$g$$

Question 19

.

Accepted Answer

The Quotient and Chain Rules

Answer

Only the Quotient Rule

Answer

The Quotient and Product Rules

Answer

Only the Chain Rule

Question 20

Which rule would you need to use?

Accepted Answer

Chain Rule

Answer

Power Rule

Answer

Product Rule

Answer

Quotient Rule

Question 21

Which rule would you need to use?

Accepted Answer

Chain Rule

Answer

Power Rule

Answer

Product Rule

Answer

Quotient Rule

Question 22

What is f'(x) if f(x) = cos(5x⁴)?

Accepted Answer

f'(x) = -20x³ sin(5x⁴)

Answer

f'(x) = sin(20x³)

Answer

f'(x) = 20x³ sin(5x⁴)

Answer

f'(x) = -sin(20x³)

Question 23

Differentiate:
f(x) = x⁷ (5 + 8x)³

Accepted Answer

f '(x) = 24x⁷(5+8x)²+7x⁶(5+8x)³

Answer

f '(x) = 168x⁶(5+8x)²

Answer

f '(x) = 3x⁷(5+8x)²+7x⁶(5+8x)³

Answer

f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Question 24

Approximate the instantaneous rate of change of the function at x = -1.

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

Accepted Answer

-4

Answer

-1/4

Answer

3

Answer

-2

Question 25

Find the instantaneous rate of change for f(x) at x = 2 for $$f\left(x\right)\ =-\frac{3}{4}x^4+2$$

Accepted Answer

-24

Answer

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

Answer

24

Answer

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

Question 26

The slope of a function is described by its ____________.

Accepted Answer

first derivative

Answer

second derivative

Answer

third derivative

Answer

expression

Question 27

Question 27.

Accepted Answer

Too Good At Goodbyes

Answer

No Goodbyes

Answer

The Last Of Goodbyes

Answer

Goodbye For Now

Question 28

Question 28.

Accepted Answer

Into the Unknown

Answer

Into the Sun

Answer

Still Into You

Answer

Into the Fire

Question 29

Question 29.

Accepted Answer

Call Me Maybe

Answer

Call Me Angel

Answer

Don't Call Me Up

Answer

Call Me Back

Question 30

Guess the song...

Accepted Answer

Perfect by Ed Sheeran

Answer

Dive by Ed Sheeran

Answer

Photograph by Ed Sheeran

Answer

How Would You Feel by Ed Sheeran

Question 31

Guess the song...

Accepted Answer

More Than Words by Extreme

Answer

Yellow by Coldplay

Answer

The Reason by Hoobstank

Answer

All of Me by John Legend

Question 32

Question 32.

Accepted Answer

Just The Way You Are

Answer

Wherever You Are

Answer

As You Are

Answer

There You Are

Question 33

Guess the song

2.

Accepted Answer

Bad guy

Answer

Lovely

Answer

Ocean eyes

Answer

Happier than ever

Question 34

Guess the song

3.

Accepted Answer

My heart will go on

Answer

How Does a Moment Last Forever

Answer

The Power of Love

Answer

Ashes

Question 35

Guess the song

5.

Accepted Answer

BOOMBAYAH

Answer

Flowers

Answer

LALISA

Answer

Pink Venom

Question 36

Guess the song

6.

Accepted Answer

Rolling in the Deep

Answer

Hello

Answer

Easy on Me

Answer

Set Fire to the Rain

Question 37

Guess the song

7.

Accepted Answer

Perfect

Answer

Happier

Answer

Thinking Out Loud

Answer

Shape of You

Question 38

Guess the song

8.

Accepted Answer

Blank Space

Answer

22

Answer

I Knew You Were Trouble

Answer

Look What You Made

Me Do

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