Chapter 9 Differentiation - Year 2 Flashcards
1
Q
A
Cosx
2
Q
A
-sinx
3
Q
What happens if there is something inside the brackets of sin or cos?
A
The k will pop out
4
Q
A
5
Q
A
6
Q
A
7
Q
A
8
Q
A
9
Q
A
10
Q
A
11
Q
What are the 3 rules of differentiation?
A
Chain rule
Product rule
Quotient rule
12
Q
What is the long version of the chain rule?
A
13
Q
A
14
Q
How do you find dydx when the function is in terms of y?
A
15
Q
What is the short version of the chain rule?
A
Bring the power to the front then lower it by 1 and multiply by the derivative of inside the brackets
16
Q
What is the product rule?
A
17
Q
What are the answers to this equation?
Why?
A
Because e^x has an asymptote when x=0 so there are no solutions
18
Q
A
19
Q
A
20
Q
A
21
Q
A
22
Q
A
23
Q
A
24
Q
A
25
26
How do you prove that:
27
How do you prove that:
28
How do you prove that the derivative of sinx is cosx?
Small angle approximations
29
What is the quotient rule?
30
How do you do parametric differentiation?
31
How do you do implicit differentiation?
Differentiate each term normally, if there is a y term then you write dy/dx after it
Rearrange to find dy/dx
32
What do i always forget to do with implicit differentiation?
Differentiate the constant on the other side of the equal sign down to 0
33
34
What do I always forget to do when differentiating cos^2x?
Have the negative sign
35
What is a point of inflection?
When the curve changes from convex to concave
36
When is there a maximum point?
f''(x)<0
Concave
37
When is there a minimum point?
f''(x)>0
Convex
