Unit 3 - More Derivatives

Question 1

Chain Rule

Answer 1

f(g(x)) = f’(g(x))*g’(x)

Question 2

Chain Rule (notation)

Answer 2

dy/dx = dy/du*du/dx

Question 3

Finding dy/dx parametrically

Answer 3

dy/dx = (dy/dt) / (dx/dt)

Question 4

(f^-1)’(b) =

Answer 4

1/f’(a)

Question 5

Derivatives of inverse functions (definition)

Answer 5

If f is differentiable at every point on interval I and f’(x) is never zero on I, then f has an inverse and f^-1 is differentiable at every point on interval I

Question 6

d/dx(sin^-1x)

Answer 6

1/sqrt(1-x^2)

Question 7

d/dx(tan^-1x)

Answer 7

1/(1+x^2)

Question 8

d/dx(sec^-1x)

Answer 8

1/(|x|sqrt(x^2-1))

Question 9

d/dx(cos^-1x)

Answer 9

pi/2 - sin^-1(x)

Question 10

d/dx(cot^-1x)

Answer 10

pi/2 - tan^-1(x)

Question 11

d/dx(csc^-1x)

Answer 11

pi/2 - sec^-1(x)

Question 12

Calculator conversion -
d/dx(sec^-1x)

Answer 12

cos^-1(1/x)

Question 13

Calculator conversion -
d/dx(cot^-1x)

Answer 13

pi/2 - tan^-1(x)

Question 14

Calculator conversion -
d/dx(csc^-1x)

Answer 14

sin^-1(1/x)

Question 15

d/dx(e^x)

Answer 15

e^x

Question 16

d/dx(a^u)

Answer 16

a^uln(a)du/dx for a>0 and a doesn’t equal 1

Question 17

d/dx(lnu)

Answer 17

1/u*du/dx

Question 18

d/dx(log_a(u))

Answer 18

1/(ulna)du/dx for a>0 and a doesn’t equal 1