Inverse Trig Derivatives

Question 1

Find f’(x)
f(x)= tan⁻¹(x)

Answer 1

f’(x)= 1/(1 + x²)
Domain is All Reals

Question 2

Find g’(x)
g(x)= sin⁻¹(x)

Answer 2

g’(x)= 1/√(1 - x²)
Domain is -1 < x < 1

Question 3

Find k’(x)
k’(x)= cos⁻¹(x)

Answer 3

k’(x)= -1/√(1 - x²)
Domain is -1 < x < 1

Question 4

Find b’(x)
b(x)= sec⁻¹(x)

Answer 4

b’(x)= 1/ x*√(x² - 1)
Domain is |x| > 1

Question 5

-CHAIN RULE-
Find h’(x)
h(x)= [f of g]

Answer 5

h’(x)= f’(g[x])*g’(x)