Inverse Trig Derivative Formula
Now we have learnt how to differentiate the Inverse Trigonometric Functions, hence we will look now the formulas for the derivative of the inverse trigonometric functions which can be used directly in the problems. Given below is the table of derivative of inverse trigonometric function formula.
Function | Derivative |
|---|---|
| sin-1x | [Tex]\frac{1}{\sqrt{1-x^2}} [/Tex] |
| cos-1x | [Tex]\frac{-1}{\sqrt{1-x^2}} [/Tex] |
| tan-1x | [Tex]\frac{1}{{1+x^2}} [/Tex] |
| cot-1x | [Tex]\frac{-1}{{1+x^2}} [/Tex] |
| sec-1x | [Tex]\frac{1}{|x|\sqrt{x^2-1}} [/Tex] |
| cosec-1x | [Tex]\frac{-1}{|x|\sqrt{x^2-1}} [/Tex] |
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Derivative of Inverse Trig Functions
Derivative of Inverse Trig Function refers to the rate of change in Inverse Trigonometric Functions. We know that the derivative of a function is the rate of change in a function with respect to the independent variable. Before learning this, one should know the formulas of differentiation of Trigonometric Functions. To find the derivative of the Inverse Trigonometric Function, we will first equate the trigonometric function with another variable to find its inverse and then differentiate it using the implicit differentiation formula.
In this article, we will learn the Derivative of Inverse Trig Functions, Formulas of Differentiation of Inverse Trig Functions, and Solve some Examples based on it. But before heading forward, let’s brush up on the concept of inverse trigonometric functions and implicit differentiation.
Table of Content
- Inverse Trigonometric Functions
- What is Implicit Differentiation?
- What is Derivative of Inverse Trigonometric Functions?
- Proof of Derivative of Inverse Trig Functions
- Inverse Trig Derivative Formula
- Inverse Trig Derivative Examples
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