Derivative Rules

Question 1

Quotient Rule Phrase

Answer 1

low d high minus high d low, square the bottom and off we go

Question 2

f(x)= mx^(n)

Answer 2

f’(x)= mnx^(n-1)

Question 3

Derivative Notation

Answer 3

f’(x) y’ (dy)/(dx) (df(x))/(dx) d/(dx)

Question 4

Product rule

Answer 4

f’(x)= f’g + g’f

Question 5

Quotient rule

Answer 5

(gf’ -fg’)/g²

Question 6

Differentiability

Answer 6

Must be continuous at x=c and left-hand derivative= right-hand derivative

Question 7

Derivative definition

Answer 7

Slope of the tangent line at a point

Question 8

f(g(x))

Answer 8

f’(g(x)) × g’(x)

Question 9

Average rate of change

Answer 9

2 places (Δy/Δx)

Question 10

Instantaneous Rate of Change

Answer 10

Derivative of function

Question 11

Matching Graphs of Functions

Answer 11

if graph 1 is f(x), then graph 2 of f’(x) will have x-intercepts at all relative extrema (max’s and min’s)

Question 12

Piecewise Functions (both differentiable and continuous)

Answer 12

1. Plug in x-values and set original equations equal too each other
2. Take derivatives of equations and set equal to each other (then plug in x-value)
3. Set up a system of equations

Question 13

Piecewise Functions (just continuous)

Answer 13

1. Plug in x-values and set equations equal to each other (repeat if more than 2 equations)
2. Set up a system of equations

Question 14

Find points where horizontal or vertical tangent line

Answer 14

f’(x) = a/ b
1. Horizontal is set a = 0
2. Vertical is set b = 0

Question 15

Average ROC

Answer 15

slope of secant line