Inverse Trig Derivative
What are Inverse Trigonometric Functions?
Inverse Trigonometric Function are the inverse of the six trigonometric functions sin, cos, tan, cosec, sec and cot. They are represented as if sin y = x then y = sin-1x
What is Inverse Trig Derivative?
Inverse Trig Derivative is the rate of change in the inverse trigonometric functions with respect to independent variable.
How to differentiate Inverse Trigonometric Functions?
We can find the derivative of inverse trigonometric by First Principle and by Implicit Differentiation Formula. The proof of the derivative of all the six inverse trigonometric functions are discussed in the article.
What is the Derivative of sin-1 x?
The derivative of sin-1x is d(sin-1x)/dx = 1/√(1 – x2) for all x ϵ (-1, 1)
What is the Derivative of cos-1x?
The derivative of cos-1x is d(cos-1x)/dx = -1/√(1 – x2) for all x ϵ (-1, 1)
What is the Derivative of tan-1x?
The derivative of tan-1x is d(tan-1x)/dx = 1/(1 + x2) for all x ϵ R
What is the Derivative of cosec-1x?
The derivative of cosec-1x is d(cosec-1x)/dx = -1/{|x|√(x2 – 1)} for all x ϵ R – [-1, 1]
What is the Derivative of sec-1x?
The derivative of sec-1x is d(sec-1x)/dx = 1/{|x|√(x2 – 1)} for all x ϵ R – [-1, 1]
What is the Derivative of cot-1x?
The derivative of cot-1x is d(cot-1x)/dx = -1/(1 + x2) for all x ϵ R
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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