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Inverse trigonometric derivatives

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Inverse trigonometric derivatives

$\frac{d}{d x} \sin^{- 1} x = \frac{1}{\sqrt{1 - x^{2}}}$ $\frac{d}{d x} \csc^{- 1} x = - \frac{1}{x \sqrt{x^{2} + 1}}$

$\frac{d}{d x} \cos^{- 1} x = - \frac{1}{\sqrt{1 - x^{2}}}$ $\frac{d}{d x} \sec^{- 1} x = \frac{1}{x \sqrt{x^{2} + 1}}$

$\frac{d}{d x} \tan^{- 1} x = \frac{1}{1 + x^{2}}$ $\frac{d}{d x} \cot^{- 1} x = - \frac{1}{1 + x^{2}}$

Index

Chapter 5 - Inverse Functions

Chapter 7 - FFR - Anti-derivatives

Chapter 8 - Inverses Revisited

Glossary and deeper reading · 1 refreshers

These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.

Derivative
A derivative gives the instantaneous rate of change of a function with respect to its input. At a point, it is the finite limit of the difference quotient when that limit exists. For example, the derivative of x² is 2x, so the tangent slope at x=3 is 6. A derivative function collects those rates across the inputs where the function is differentiable.
Read more: 2.2 · Derivative →

Derivative

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