Derivative of Inverse Trig

Question 1

f’(sin^1 x)

Answer 1

1 / SQRT(1 - x^2)

Question 2

f’(cos^1 x)

Answer 2

-1 / SQRT(1 - x^2)

Question 3

f’(tan^-1 x)

Answer 3

1 / (1 + x^2)

Question 4

f’(csc^1 x)

Answer 4

-1 / x(SQRT(x^2 - 1))

Question 5

f’(sec^1 x)

Answer 5

1 / x(SQRT(x^2 - 1))

Question 6

f’(cot^-1 x)

Answer 6

-1 / (1+x^2)

Question 7

Easiest way to remember which is positive and negative?

Answer 7

The 3 “normal” trig functions (sin, cos, tan) are all positive.
The other 3 are negative.

Question 8

Easiest way to remember the formulas?

Answer 8

Sin + csc are same
Cos + sec are same
Tan + cot are same
(except for positive / negative out front)