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

**Related Pages**

Lessons On Trigonometry

Inverse trigonometry

Trigonometric Derivatives

Calculus: Derivatives

Calculus Lessons

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

- f(x) = (sin
^{-1})^{2} - g(t) = cos
^{-1}√(2t - 1) - 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 + x^{2})

**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.

- f(x) = 3sin
^{-1}(x) - g(x) = 4cos
^{-1}(3x^{2})

**Derivatives of Inverse Trig Functions**

**Examples:**

Find the derivatives of each given function.

- f(x) = -2cot
^{-1}(x) - g(x) = 5tan
^{-1}(2^{x})

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.