2.1-2.5 quiz Flashcards

1
Q

sin x ‘

A

cos x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

cos x’

A

-sin x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

tan x’

A

sec^2 x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

cot x

A

-csc^2 x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

sec x’

A

sec x(tan x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

csc x’

A

-csc x(cot x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

product rule

h(x) = f(x)(g(x))

A

h’(x) = f x g’ + g x f’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

quotient rule

h(x) = f(x)/g(x)

A

h’(x) = g x f’ - f x g’ / g^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

chain rule

h(x) = f(g(x))

A

think like peeling an onion

h’(x) = f’(g(x)) x g’(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

sin 2x

A

2sinxcosx

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

consider the curve : formula

show that dy/dx equals formula

A

basically dy/dx is the formula of the curve

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

what is differentiation

A

where the slope equals the tangent line

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

the process of finding a derivative is called

A

differentiation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

what does differentiability imply

A

continuity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

the derivative doesn’t exist at

A

discontinuities
cusps
when the tangent becomes vertical(straight up and down line part)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

power rule

d/dx[x^n] =

A

nx^n-1

17
Q

power rule on constants

d/dx 5

A

0

18
Q

find equation of tangent line to graph of f(x) at the point(x,y)

how to solve

A

find derivative of f(x) to solve for the slope at any point on the function

then plug in (x,y) to find the slope for that particular point

19
Q

implicit differentiation procedure

A

differentiate each term with respect to x (dy/dx)

nivel all terms contains dy/dx to the left side of the equation and all other terms to the right side

factor out dy/dx on left side of equation

solve for dy/dx

20
Q

product vs chain tule for trig functions:

A

if the angle theta is just x it is product rule; if it is 2x however or (2x-1) whether it has parentheses or not it is chain rule

21
Q

what happens to the “y” with implicit differentiation

A

it becomes dy/dx

with respect to x

22
Q

what happens to x in implicit differentiation

A

nothing with respect to x becomes 1 so the x is left alone

23
Q

L’hospitsl rule

How to wrote AP TESTA ND FRQ

A

1) show f(x) and g(x) are continuos and differentiable
(Write f(x) and g(x) separately!)

2) show lim f(x) = 0 and lim g(x) = 0
x->a x-> a
3) using L’Hospitals rule
lim f(x)/ g(x) = lim f’(x)/g’(x) plug in number
x->a x-> a

24
Q

L’hospital rule idea

A

If in indeterminate form find derivative of og equation and replug in pts, if still indeterminate keep finding derivatives

25
Q

finding second derivative

A

determine what is f(x) and g(x) and f’(x) and g’(x) [still use implicit differentiation plug in dy/dx]

then solve

for the dy/dx (it equals previous derivative
D’)

26
Q

derivative of “xy”

A

use product rule

(xdy/dx + y1)

keep subtraction sign outside of parentheses and distribute once finished differentiating

27
Q

constant on right side of equal sign

A

don’t forget to differentiate it!!

equals 0

28
Q

how to write second differentiation in (dy/dx) format

A

d^2y/dx^2

??

29
Q

when solving any typa derivative problem

A

first identify and write down f(x), f’(x), g(x), g’(x)

then identify what rule to use and write that down
write down formula for rule too if needed

30
Q

differentiation of 4xy

A

group (4x) as f(x) and (y) as g(x)

becuase 4 is only multiplied to the y(not distributed to the whole thing)

31
Q

when doing implicit differentiation only put derivatives on y when

A

differentiating for y

for example in product rule where f(x)*g’(x) if f(x) = y DONT put dy/dx becuase u aren’t supposed to find the derivative of f(x)

differentiating is ONLY used when u need to find the derivative of THAT PARTICULAR variable

32
Q

is cos^2(x) composite

A

yes

inner function: cos(x)

outer function: x^2

33
Q

derivative of sec(4x)

A

sec(4x)tan(4x)*4

34
Q

trig function inside of trig function means how many parts of an onion

A

3 layers of onion

35
Q
lim     f(x+h) -f(x)/ x-h
x->h

identify

derivative of f(x) @ any point

A

derivative of f(x) @ any point is the derivative upper right part of the fraction

f’(x)

36
Q

instantaneous rate of change

A

find derivative

then plug in point

37
Q

average rate of change

A

f(b)-f(a)/ b-a