Derivatives

Question 1

Explain the derivative formula. Draw it out.

Answer 1

Question 2

Answer 2

Question 3

What are the notations for a derivative of a function and a derivative of a point?

Answer 3

Question 4

When is a function diferentiable?

Answer 4

Question 5

Use basic Derivative rules

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Question 6

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Question 7

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Question 8

Proof of the sum/difference rule of derivatives?

Answer 8

Question 9

The power rule?

Answer 9

Question 10

Constant Multiple Derivative Rule

Answer 10

Question 11

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Question 13

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Question 14

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Question 15

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Question 16

What is the derivative of sin(x)

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Question 17

What is the product rule?

Answer 17

Question 18

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Question 19

What is the quotent rule?

Answer 19

Question 20

What is the derivative of tan(x)

Answer 20

Question 21

What are the trig function derivatives?

Answer 21

Question 22

Saying for rembering product of a derivative?

Answer 22

Question 23

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Question 24

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Question 25

What is the chain rule?

Answer 25

Question 26

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Question 27

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Question 28

Find the derivative of Y with respect to X

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Question 29

Find the derivative and explain it using lebienze notation

Answer 29

Question 30

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Question 31

Explain this functions using the chain rule and liezben notation

Answer 31

Question 33

Answer 33

Second Derivative with implicited diferentiaition

Question 34

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Question 35

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Question 37

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Question 39

What is the derivatives of the natural log and logbase a?

Answer 39

Question 40

Answer 40

Use logarithimic differentiation. Notice there is a variable in as an exponent and base!

Question 41

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Question 42

What are the derivaives rules for exponents and logs and ln

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Question 43

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Question 44

What are critcal points?

Answer 44

X=0 is a critical point becuase the tangent line goes to 0. at points -3 and 3 they are undefined in the actual function so they cannot be critical points

Question 45

watch out for this

Answer 45

when taking the log of something, make sure you ultiply that entire exponent back onto the log

Question 46

Find the critical point?

Answer 46

Question 47

What is the mean value theorum? how does it look on a graph. What is the formula?

Answer 47

Question 49

Describe the extreame value therom

Answer 49

Question 50

What are the absolue max mins and local max mins?

Answer 50

Question 51

Explain concavity using graphs of the first and second derivitives.

Answer 51

the first deriviates shows over the purple bit that the slope is decreasing. the first derivites shows this. Ones the slope of the graph stops decreasing the first derviive become zero because no change is happining and it starts increasing. This is why setting the second deriviative to zero gives us inflections point. the slope of the first dervite become zero.

Question 52

What is the inflection point?

Answer 52

Point on in the function where the slope changes from either increasing or decreasing

Question 53

how can you prove if a function is deacreasing or decreasing?

Answer 53

Question 54

When sketching a function what is everything you should find?

Answer 54

Question 55

What is the first derivative test? And the the increasing/ decreasing test?

Answer 55