Midterm #2

Question 1

What is the derivative of arctan

Answer 1

u’ / (1 + u^2)

Question 2

What is the derivative of arccos

Answer 2

-u’ / (sqrt(1 - u^2))

Question 3

What is the derivative of arcsin

Answer 3

u’ / (sqrt(1 - u^2))

Question 4

derivative of arccsc

Answer 4

• u’ / (abs(u)sqrt(u^2 - 1))

Question 5

derivative of arcsec

Answer 5

u’ / (abs(u)sqrt(u^2 -1))

Question 6

derivative of arccot

Answer 6

• u’ / (1 + u^2)

Question 7

derivative of a logarithm

Answer 7

u’ / (u * ln(a)))

where “a” was the base of the logarithm

Question 8

Rolles Thm

Answer 8

Hypotheses:

1. cont. over closed bounded interval [a,b]
2. differentiable over open interval
3. f(a) = f(b)

conclusion:
f’(c) = 0

Question 9

M.V.T.

Answer 9

Hypotheses:

1. cont. on closed int (a,b)
2. differentiable on open interval

Conclusion:
f’(c) = ( f(b) - f(a) ) /( b - a )

Question 10

derivative of tan

Answer 10

sec^2

Question 11

derivative of sec

Answer 11

tan*sec

Question 12

derivative of csc

Answer 12

-cot*csc

Question 13

derivative of cot

Answer 13

-csc^2