Chapter 2

Question 1

Difference quotient

Answer 1

(f (x+h) - f (x)) / h

Question 2

Derivative

Answer 2

The instantaneous rate of change of a function w/ respect to another variable

Question 3

The slope of the tangent to f at x = c

Answer 3

f ‘ (c) = the derivative of the function at that particular point

Question 4

Common derivative notation

Answer 4

f ‘ (x) or d / dx

Question 5

d/dx (sin x)

Answer 5

cos x

Question 6

d/dx (cos x)

Answer 6

-sin x

Question 7

d/dx (e^x)

Answer 7

e^x

Question 8

d/dx (ln x)

Answer 8

1/x

Question 9

Derivative of a constant (d/dx (c))

Answer 9

= 0

Question 10

d/dx (1/x)

Answer 10

-1/x^2 or -x^-2 ….but -1/x^2 is preferred

Question 11

d/dx ( sq rt (x))

Answer 11

1 / 2 sq rt x

Question 12

Equation for a line through (x_1, y_1) with slope ‘m’

Answer 12

y - y_1 = m (x - x_1)

Question 13

a position function

Answer 13

s(t)

Question 14

a velocity

Answer 14

v(t)…..which equals s’(t) = derivative of position function

Question 15

an acceleration

Answer 15

a(t)…..which equals v’(t) and s’‘(t) = derivative of a velocity function and second derivative of position function

Question 16

d/dx (tan x)

Answer 16

sec² x

Question 17

d/dx (sec x)

Answer 17

sec x tan x

Question 18

d/dx (cot x)

Answer 18

-csc² x

Question 19

d/dx (csc x)

Answer 19

-csc x cot x

Question 20

The chain rule

Answer 20

(Derivative of outer function) x (derivative of inner function)
y’ = f’ (g(x)) times g’ (x)

Question 21

Generalized power rule

Answer 21

d/dx (g(x)^n) = n (g(x))^n-1 times g’ (x)

Question 22

Quotient Rule

Answer 22

(f/g)’ = (f ‘g - f g’) / g²
or
d/dx (f(x)/g(x)) = (g(x) f ‘(x) - f(x) g’(x)) / [g(x)]²

Question 23

Product Rule

Answer 23

(fg)’ = f ‘g + fg’
(fgh)’ = f ‘gh + fg’h + fgh’
etc.