The Chain Rule with Exponentials and Logarithms

Question 1

A student writes ddx[e^8x] = e^8x. What, if anything, is wrong?

Accepted Answer

The factor 8 is missing: the derivative is 8e^8x

Answer

Nothing is missing; the work is correct

Answer

The exponent should have been lowered, giving 8xe^8x - 1

Answer

The factor 8 is missing

Question 2

Find the derivative of w(x) = (x^3 - 4), on an interval where the argument is positive.

Accepted Answer

w'(x) = 3x^2x^3 - 4

Answer

w'(x) = 1x^3 - 4

Answer

w'(x) = 3x^23x^2

Answer

w'(x) = (3x^2)

Question 3

A student writes ddx[(7x)] = 17x. What, if anything, is wrong?

Accepted Answer

The numerator is wrong: the derivative is 77x, which simplifies to 1x

Answer

Nothing is wrong; the work is correct

Answer

The answer should be (7)

Answer

The answer should be 17

Question 4

Find the derivative of q(x) = 3^4x.

Accepted Answer

q'(x) = 4(3^4x)3

Answer

q'(x) = (3^4x)3

Answer

q'(x) = 4(3^4x)

Question 5

Find the derivative of f(x) = e^-6x^2 + 8.

Accepted Answer

f'(x) = (-12x)e^-6x^2 + 8

Answer

f'(x) = e^-6x^2 + 8

Answer

f'(x) = (-12x)e^-12x

Answer

f'(x) = (-6x^2 + 8)e^-6x^2 + 8

Question 6

A student writes ddx[(2x)] = 12x. What, if anything, is wrong?

Accepted Answer

The numerator is wrong: the derivative is 22x, which simplifies to 1x

Answer

Nothing is wrong; the work is correct

Answer

The answer should be (2)

Answer

The answer should be 12

Question 7

Find the derivative of q(x) = e^8x + 7.

Accepted Answer

q'(x) = (8)e^8x + 7

Answer

q'(x) = e^8x + 7

Answer

q'(x) = (8)e^8

Answer

q'(x) = (8x + 7)e^8x + 7

Question 8

Find the derivative of r(x) = (-2x^3 + 8), on an interval where the argument is positive.

Accepted Answer

r'(x) = -6x^2-2x^3 + 8

Answer

r'(x) = 1-2x^3 + 8

Answer

r'(x) = -6x^2-6x^2

Answer

r'(x) = (-6x^2)

Question 9

Find the derivative of w(x) = (-7x^3 + 4), on an interval where the argument is positive.

Accepted Answer

w'(x) = -21x^2-7x^3 + 4

Answer

w'(x) = 1-7x^3 + 4

Answer

w'(x) = -21x^2-21x^2

Answer

w'(x) = (-21x^2)

Question 10

Find the derivative of w(x) = e^5x^3 - 7.

Accepted Answer

w'(x) = (15x^2)e^5x^3 - 7

Answer

w'(x) = e^5x^3 - 7

Answer

w'(x) = (15x^2)e^15x^2

Answer

w'(x) = (5x^3 - 7)e^5x^3 - 7

Question 11

Find the derivative of f(x) = (8x^2 + 5).

Accepted Answer

f'(x) = 16x8x^2 + 5

Answer

f'(x) = 18x^2 + 5

Answer

f'(x) = 16x16x

Answer

f'(x) = (16x)

Question 12

Find the derivative of p(x) = e^-9x^3 - 7.

Accepted Answer

p'(x) = (-27x^2)e^-9x^3 - 7

Answer

p'(x) = e^-9x^3 - 7

Answer

p'(x) = (-27x^2)e^-27x^2

Answer

p'(x) = (-9x^3 - 7)e^-9x^3 - 7

Question 13

Find the derivative of g(x) = e^8x + 3.

Accepted Answer

g'(x) = (8)e^8x + 3

Answer

g'(x) = e^8x + 3

Answer

g'(x) = (8)e^8

Answer

g'(x) = (8x + 3)e^8x + 3

Question 14

Find the derivative of r(x) = _5(-4x + 1), where the argument is positive.

Accepted Answer

r'(x) = -4(-4x + 1)5

Answer

r'(x) = 1(-4x + 1)5

Answer

r'(x) = -4-4x + 1

Answer

r'(x) = -45-4x + 1

Question 15

Find the derivative of s(x) = (x^2 + 3).

Accepted Answer

s'(x) = 2xx^2 + 3

Answer

s'(x) = 1x^2 + 3

Answer

s'(x) = 2x2x

Answer

s'(x) = (2x)

Question 16

A student writes ddx[e^9x] = e^9x. What, if anything, is wrong?

Accepted Answer

The factor 9 is missing: the derivative is 9e^9x

Answer

Nothing is missing; the work is correct

Answer

The exponent should have been lowered, giving 9xe^9x - 1

Answer

The factor 9 is missing

Question 17

Find the derivative of g(x) = (x^3 + 8), on an interval where the argument is positive.

Accepted Answer

g'(x) = 3x^2x^3 + 8

Answer

g'(x) = 1x^3 + 8

Answer

g'(x) = 3x^23x^2

Answer

g'(x) = (3x^2)

Question 18

Find the derivative of s(x) = e^6x + 5.

Accepted Answer

s'(x) = (6)e^6x + 5

Answer

s'(x) = e^6x + 5

Answer

s'(x) = (6)e^6

Answer

s'(x) = (6x + 5)e^6x + 5

Question 19

Find the derivative of w(x) = (-5x^3 - 7), on an interval where the argument is positive.

Accepted Answer

w'(x) = -15x^2-5x^3 - 7

Answer

w'(x) = 1-5x^3 - 7

Answer

w'(x) = -15x^2-15x^2

Answer

w'(x) = (-15x^2)

Question 20

Find the derivative of p(x) = 3^8x.

Accepted Answer

p'(x) = 8(3^8x)3

Answer

p'(x) = (3^8x)3

Answer

p'(x) = 8(3^8x)

Question 21

Find the derivative of w(x) = _10(9x + 1), where the argument is positive.

Accepted Answer

w'(x) = 9(9x + 1)10

Answer

w'(x) = 1(9x + 1)10

Answer

w'(x) = 99x + 1

Answer

w'(x) = 9109x + 1

Question 22

Find the derivative of v(x) = 2^6x.

Accepted Answer

v'(x) = 6(2^6x)2

Answer

v'(x) = (2^6x)2

Answer

v'(x) = 6(2^6x)

Question 23

Find the derivative of f(x) = e^-4x^3 - 6.

Accepted Answer

f'(x) = (-12x^2)e^-4x^3 - 6

Answer

f'(x) = e^-4x^3 - 6

Answer

f'(x) = (-12x^2)e^-12x^2

Answer

f'(x) = (-4x^3 - 6)e^-4x^3 - 6

Question 24

Find the derivative of f(x) = (5x + 1), on an interval where the argument is positive.

Accepted Answer

f'(x) = 55x + 1

Answer

f'(x) = 15x + 1

Answer

f'(x) = 55

Answer

f'(x) = (5)

Question 25

A student writes ddx[(3x)] = 13x. What, if anything, is wrong?

Accepted Answer

The numerator is wrong: the derivative is 33x, which simplifies to 1x

Answer

Nothing is wrong; the work is correct

Answer

The answer should be (3)

Answer

The answer should be 13

Question 26

Find the derivative of w(x) = (2x^2 - 3), on an interval where the argument is positive.

Accepted Answer

w'(x) = 4x2x^2 - 3

Answer

w'(x) = 12x^2 - 3

Answer

w'(x) = 4x4x

Answer

w'(x) = (4x)

Question 27

Find the derivative of w(x) = e^-8x^3 + 7.

Accepted Answer

w'(x) = (-24x^2)e^-8x^3 + 7

Answer

w'(x) = e^-8x^3 + 7

Answer

w'(x) = (-24x^2)e^-24x^2

Answer

w'(x) = (-8x^3 + 7)e^-8x^3 + 7

Question 28

A student writes ddx[(9x)] = 19x. What, if anything, is wrong?

Accepted Answer

The numerator is wrong: the derivative is 99x, which simplifies to 1x

Answer

Nothing is wrong; the work is correct

Answer

The answer should be (9)

Answer

The answer should be 19

Question 29

Find the derivative of f(x) = _3(8x + 1), where the argument is positive.

Accepted Answer

f'(x) = 8(8x + 1)3

Answer

f'(x) = 1(8x + 1)3

Answer

f'(x) = 88x + 1

Answer

f'(x) = 838x + 1

Question 30

Find the derivative of v(x) = e^9x^3 + 8.

Accepted Answer

v'(x) = (27x^2)e^9x^3 + 8

Answer

v'(x) = e^9x^3 + 8

Answer

v'(x) = (27x^2)e^27x^2

Answer

v'(x) = (9x^3 + 8)e^9x^3 + 8

BLASTROOM

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BLASTROOM

The Chain Rule with Exponentials and Logarithms

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The Chain Rule with Exponentials and Logarithms

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner