Inverse Trig Derivatives Formulas

Derivative of an inverse function

(f⁻¹)'(x) = 1 / f'(f⁻¹(x))

How do you find (f⁻¹)'(b)?

1. Solve f(a) = b

2. Find f'(a)

3. (f⁻¹)'(b) = 1 / f'(a)

d/dx [arcsin(u)]

u' / √(1 − u²)

d/dx [arccos(u)]

−u' / √(1 − u²)

d/dx [arctan(u)]

u' / (1 + u²)

d/dx [arcsec(u)]

u' / (|u|√(u² − 1))

d/dx [arccsc(u)]

−u' / (|u|√(u² − 1))

d/dx [arccot(u)]

−u' / (1 + u²)

d/dx [sin x]

cos x

d/dx [cos x]

−sin x

d/dx [tan x]

sec²x

d/dx [csc x]

−csc x cot x

d/dx [sec x]

sec x tan x

d/dx [cot x]

−csc²x