Lecture 13

Question 1

What is the general formula for the chain rule?

Answer 1

f[g(x)]=f’[g(x)] * g’(x)

Question 2

what is the derivative of sine?

Answer 2

cosine

Question 3

what is the derivative of cosine?

Answer 3

-sine

Question 4

what is the derivative of tan?

Answer 4

sec^(2)(x)

Question 5

what is the formula to find the inverse derivative?

Answer 5

(f-1)’(x)=1/f’[(f-1)(x)]

Question 6

what is the domain of tan

Answer 6

(-pi/2,pi/2)

Question 7

what is the derivative of arcsin?

Answer 7

1/square root of 1+x^(2)

Question 8

what is the derivative of arccos?

Answer 8

-1/square root of 1+x^(2)

Question 9

if given a table, one for x, f(x) and f’(x), how do you find the inverse derivative of (f-1)’(3) for instance?

Answer 9

1. write the inverse derivative formula
2. plug the value into the inverse derivative formulas
3. use the inverse derivative formula and the table to guide you starting from the right side of the denominator of the formula

Question 10

a store sells 150 chocolates for $40 dollar. If the price were lowered to $35, they would sell 160 chocolates per month. S(p) is the number of chocolates sold each month when the price is p dollars. Multiple formulas are given to choose from. What should you do to choose the formula this scenario creates?

Answer 10

1. find the difference in money
2. find the difference in chocolate
3. use those answers to piece together what the equation is

Question 11

how do you find the equation of a quadratic given a function and an x value?

Answer 11

1. plug the x value into the original function
2. find the first derivative of the original function then plug in the x value
3. find the second derivative of the original function then plug in the x value
4. find the first derivative of the quadratic formula then plug in the x value
5. find the second derivative of the quadratic formula then plug in the x value
6. try to solve for one of the variables
7. plug the variable value into another equation to find another variable
8. keep plugging in what you know to find all the variables
9. create the equation