Tuest - 3.3, 3.5, 4.1, 4.2, 4.4

Question 1

d/dx sin(x)

Answer 1

cos(x)

Question 2

d/dx cos(x)

Answer 2

−sin(x)

Question 3

d/dx tan(x)

Answer 3

sec²(x)

Question 4

d/dx sec(x)

Answer 4

sec(x)tan(x)

Question 5

d/dx cot(x)

Answer 5

−csc^2(x)

Question 6

d/dx csc(x)

Answer 6

−csc(x)tan(x)

Question 7

Derivatives: Constant Rule

Answer 7

d/dx [c] = 0

Question 8

Derivatives: Constant Multiple Rule

Answer 8

d/dx [cf(x)] = cf ‘(x)

Question 9

Derivatives: Sum Rule

Answer 9

d/dx [f(x) + g(x)] = f ‘(x) + g ‘(x)

Question 10

Derivatives: Difference Rule

Answer 10

d/dx [f(x) - g(x)] = f ‘(x) - g ‘(x)

Question 11

Derivatives: Product Rule

Answer 11

d/dx [f(x)g(x)] = f ‘(x)g(x) + g ‘(x)f(x)

Question 12

Derivatives: Quotient Rule

Answer 12

d/dx [f(x) / g(x)] = [g(x)f ‘(x) + f(x)g ‘(x)] / [g(x)]²

Question 13

Derivatives: Chain Rule

Answer 13

d/dx [f(g(x))] = f ‘(g(x))g’(x)

Question 14

g’(y) = 1/f’(x)

Answer 14

is also f^-1(b) = 1/f’(a)

Question 15

a^y = b

Answer 15

loga(b) = y

Question 16

Derivative of Natural Logs

Answer 16

d/dx [lnx] = 1/x

Question 17

Derivative of e^x

Answer 17

d/dx [e^x] = e^x

Question 18

Derivative of [loga(x)]

Answer 18

d/dx [loga(x)] = 1/(xlna)

Question 19

Derivative of a Power

Answer 19

d/dx [a^x] = (a^x )lna

Question 20

ASTC

Answer 20

Positivity:

All - 1st Q
Sin/Csc - 2nd Q
Cos/Sec - 3rd Q
Tan/Cot - 4th Q

Question 21

Log of a Base raised to a Power

Answer 21

loga(a^x) = x

Question 22

Base Change Formula: Base B

Answer 22

loga(x) = logb(x) / logb(a)

Question 23

Base Change Formula: Base 10

Answer 23

loga(x) = log(x) / log(a)

Question 24

Base Change Formula: Base e

Answer 24

loga(x) = ln(x) / ln(a)

Question 25

Law of Logs: Multiplication

Answer 25

loga(UV) = loga(U) + loga(V)

Question 26

Law of Logs: Division

Answer 26

loga(U/V) = loga(U) − loga(V)

Question 27

Law of Logs: Power

Answer 27

loga(u^n) = nloga(u)