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Home / Mathematics / Derivative of Inverse Trigonometric Functions

SAT Derivative of Inverse Trigonometric Functions

Last Updated on Mar 03, 2025
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Notation for Inverse Trigonometric Functions:

The inverse trigonometric functions are typically denoted by prefixing 'arc' to the trigonometric function or by raising the function to the power of -1. For instance, the inverse of sin x can be written as:

arcsin(x) or

 

Now, let's dive into the process of deriving the inverse of a trigonometric function.

Example: Let's consider the function

 

Given the function

…………(i)

 

We can rewrite it as

 

Differentiating with respect to x gives us:

 

 

Substituting the value of y from equation (i), we get

 

………..(ii)

 

It's clear from equation (ii) that cos y cannot be 0, as it would make the function undefined.

 

 

Which implies

 

From equation (i), we have

 

 

 

Using the property of trigonometric functions, we get

 

 

 

…………(iii)

 

Substituting the value from equation (iii) into equation (ii), we get

 

 

Hence, the derivative of the inverse sine function is

 

 

Derivatives of Other Inverse Trigonometric Functions
Function
arcsin x
arccos x
arctan x
arccot x
arcsec x
arccsc x

``` Please note that I've removed the video lesson and examples as per your instructions

Frequently Asked Questions

Inverse Trigonometric functions, also known as arcus functions, cyclometric functions or anti-trigonometric functions, are used to obtain angle for a given trigonometric value.

The derivative of Inverse Trigonometric function can be found by differentiating the function with respect to x. The process is explained in detail in the article with examples.

The derivative of arcsin x is 1/√(1-x^2).
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