 # Inverse Trigonometric Derivatives

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In this lesson, we will look at how to find the derivatives of inverse trigonometric functions.

### Table of Derivatives of Inverse Trigonometric Functions

The following table gives the formula for the derivatives of the inverse trigonometric functions. Scroll down the page for more examples and solutions on how to use the formulas. Example:

Differentiate Solution:

We can use the above formula and the chain rule. Example:

Differentiate Solution:

We use the product rule and chain rule. Inverse Trigonometric Functions - Derivatives
Formulas for the derivatives of the six inverse trig functions and derivative examples
Examples:
Find the derivatives of the following functions
1. f(x) = (sin-1)2
2. g(t) = cos-1√(2t - 1)
3. y = tan-1(x/a) + ln√((x-a)/(x+a))
Inverse Trigonometric Functions - Derivatives - Harder Example
Example:
Find the derivatives of
y = sec-1√(1 + x2)
Inverse Trigonometric Functions - Derivatives - Harder Example
Example:
Find the derivatives of
y = sin-1(cos x/(1+sinx))

Derivatives of Inverse Trig Functions
One example does not require the chain rule and one example requires the chain rule.
Examples:
Find the derivatives of each given function.
1. f(x) = 3sin-1(x)
2. g(x) = 4cos-1(3x2)
Derivatives of Inverse Trig Functions
Examples:
Find the derivatives of each given function.
1. f(x) = -2cot-1(x)
2. g(x) = 5tan-1(2x)

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