Unit 3B

Question 1

What is the limit of the inverse of y=sinx

Answer 1

y’=1 / (sqrt(1-x^2))

Question 2

What is the limit of the inverse of y=cosx

Answer 2

y’=-1 / (sqrt(1-x^2))

Question 3

What is the limit of the inverse of y=tanx

Answer 3

y’=1 / (x^2+1)

Question 4

What is the derivative of the inverse of y=cotx

Answer 4

y’= -csc^2(x)

Question 5

What is the limit of the inverse of y=csc(x)

Answer 5

y’= -1 / (abs(x)sqrt(x^2-1))

Question 6

What is the derivative of the inverse of y=secx

Answer 6

y’= 1 / (abs(x)sqrt(x^2-1))

Question 7

What is the chain rule?

Answer 7

f’(g(x)) = f’(g(x))*g’(x)

Question 8

What is the power rule? (Involving functions)

Answer 8

d/dx g(x)^n = n(g(x))^(n-1) * g’(x)

Question 9

Derivative of a^u(x)

Answer 9

d/dx a^(u(x)) = a^(u(x)) * ln(a)*u’(x)