Inverse Trig. Derivatives

Question 1

arc sin(x/a)

Answer 1

1/√(a^2 - x^2)

Question 2

arc cos(x)

Answer 2

-1/√(1 - x^2)

Question 3

a). arc tan(x)

b). (1/a)arc tan(x/a)

Answer 3

a). 1/(1 + x^2)

b). 1/(a^2 + x^2)

Question 4

arc csc(x)

Answer 4

-1/(∣x∣√(x^2 - 1))

Question 5

a). arc sec(x)

b). (1/a)arc sec(∣x∣/a)

Answer 5

a). 1/(∣x∣√x^2 - 1)

b). 1/(x√(x^2 - a^2))

Question 6

arc cot(x)

Answer 6

-1/(1 + x^2)