Inverse Hyperbolic functions

1 . \frac{d}{d x} \sin h^{- 1} x = \frac{1}{\sqrt{1 + x^{2}}}

2 . \frac{d}{d x} \cos h^{- 1} x = \frac{1}{\sqrt{x^{2} - 1}}

3 . \frac{d}{d x} \tan h^{- 1} x = \frac{1}{1 - x^{2}}, | x | \lt 1

4 . \frac{d}{d x} \cot h^{- 1} x = \frac{1}{x^{2} - 1}, | x | > 1

5 . \frac{d}{d x} \sec h^{- 1} x = \frac{- 1}{x \sqrt{1 - x^{2}}}, 0 \lt x \lt 1

6 . \frac{d}{d x} c o s e c h^{- 1} x = \frac{- 1}{x \sqrt{1 + x^{2}}}, x > 0

D i f f e r e n t i a t e y = \tan h^{- 1} (\sin x)

y ‘ = \frac{1}{1 - \sin^{2} x} \cdot \frac{d}{d x} (\sin x)

y ‘ = \frac{1}{1 - \sin^{2} x} \cdot \cos x

y ‘ = \frac{\cos x}{\cos^{2} x}

y ‘ = \sec x

Inverse Hyperbolic functions – Derivation formulas