Chapter 9 Differentiation - Year 2

Question 1

Answer 1

Cosx

Question 2

Answer 2

-sinx

Question 3

What happens if there is something inside the brackets of sin or cos?

Answer 3

The k will pop out

Question 4

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

What are the 3 rules of differentiation?

Answer 11

Chain rule
Product rule
Quotient rule

Question 12

What is the long version of the chain rule?

Answer 12

Question 13

Answer 13

Question 14

How do you find dydx when the function is in terms of y?

Answer 14

Question 15

What is the short version of the chain rule?

Answer 15

Bring the power to the front then lower it by 1 and multiply by the derivative of inside the brackets

Question 16

What is the product rule?

Answer 16

Question 17

What are the answers to this equation?
Why?

Answer 17

Because e^x has an asymptote when x=0 so there are no solutions

Question 18

Answer 18

Question 19

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

Answer 24

Question 25

Answer 25

Question 26

How do you prove that:

Answer 26

Question 27

How do you prove that:

Answer 27

Question 28

How do you prove that the derivative of sinx is cosx?

Answer 28

Small angle approximations

Question 29

What is the quotient rule?

Answer 29

Question 30

How do you do parametric differentiation?

Answer 30

Question 31

How do you do implicit differentiation?

Answer 31

Differentiate each term normally, if there is a y term then you write dy/dx after it Rearrange to find dy/dx

Question 32

What do i always forget to do with implicit differentiation?

Answer 32

Differentiate the constant on the other side of the equal sign down to 0

Question 33

Answer 33

Question 34

What do I always forget to do when differentiating cos^2x?

Answer 34

Have the negative sign

Question 35

What is a point of inflection?

Answer 35

When the curve changes from convex to concave

Question 36

When is there a maximum point?

Answer 36

f''(x)<0 Concave

Question 37

When is there a minimum point?

Answer 37

f''(x)>0 Convex