Unit 2 Test 3 - Derivatives (2G, 2H, 2I, 2J)

Question 1

inverse functions

Answer 1

g’(y1) = 1/(f’(x1))

Question 2

derivative of sin-1(u)

Answer 2

1/(√1-u^2) * du/dx

Question 3

derivative of cos-1(u)

Answer 3

-1/(√1-u^2) * du/dx

Question 4

derivative of tan-1(u)

Answer 4

1/(u^2 + 1) * du/dx

Question 5

derivative of cot-1(u)

Answer 5

-1/(u^2 + 1) * du/dx

Question 6

derivative of sec-1(u)

Answer 6

1/(|u|√u^2 - 1) * du/dx

Question 7

derivative of csc-1(u)

Answer 7

-1/(|u|√u^2 - 1) * du/dx

Question 8

derivative of e^x

Answer 8

e^x

Question 9

derivative of ln(x)

Answer 9

1/x

Question 10

derivative of a^u

Answer 10

a^u * ln(a) * u’

Question 11

derivative of loga(u)

Answer 11

1/(u*ln(a)) * u’