MATH 112 Exam 2 Memorization

Question 1

d/dx (b^u)

Answer 1

Question 2

d/dx (b^x) = ?

Answer 2

Question 3

ln 1 = ?

Answer 3

0

Question 4

d/dx tan x = ?

Answer 4

sec² x

Question 5

ln 0 = ?

Answer 5

Undefined. The domain of ln (and log) includes all real numbers x > 0.

Question 6

d/dx log_b (u) = ?

Answer 6

Question 7

-ln 4 = ?

Answer 7

ln 1/4

Question 8

d/dx (cos^-1 x) = ?

Answer 8

Question 9

d/dx sin x = ?

Answer 9

cos x

Question 10

d/dx cos x = ?

Answer 10

-sin x

Question 11

d/dx (cot^-1 x) = ?

Answer 11

Question 12

d/dx ln(u) = ?

Answer 12

Question 13

Remember the chain rule for composed functions!

Answer 13

Question 14

ln 1/3 = ?

Answer 14

-ln 3

Question 15

d/dx (csc^-1​ x) = ?

Answer 15

Question 16

Steps in Logarithmic Differentiation

Answer 16

Question 17

(1 - cos x) / (x) = ?

Answer 17

0

Question 18

d/dx (sec^-1​ x) = ?

Answer 18

Question 19

d/dx cot x = ?

Answer 19

-csc² x

Question 20

d/dx sec x = ?

Answer 20

sec x tan x

Question 21

d/dx (log_b x) = ?

Answer 21

Question 22

d/dx (e^u) = ?

Answer 22

Question 23

d/dx (ln x) = ?

Answer 23

Question 24

(sin x) / (x) = ?

Answer 24

1

Question 25

d/dx csc x = ?

Answer 25

-csc x cot x

Question 26

d/dx (sin^-1 x) = ?

Answer 26

Question 27

d/dx (tan^-1 x) = ?

Answer 27