Question

Find the derivative. $$ y=\left(\tan ^{-1} x\right)^{3} $$

   Find the derivative.
$$
y=\left(\tan ^{-1} x\right)^{3}
$$

Calculus: Early Transcendentals

Calculus: Early Transcendentals

Jon Rogawski, Colin… 4th Edition

Chapter 3, Problem 43

Instant Answer

Solved by Expert Audrey Fong

07/16/2021

Step 1

Here, our function is \(\left(\tan ^{-1} x\right)^{3}\), so we treat \(\tan ^{-1} x\) as our 'x' in the power rule. This gives us: \[ \frac{dy}{dx} = 3\left(\tan ^{-1} x\right)^{2} \cdot \frac{d}{dx}(\tan ^{-1} x) \] Show more…

Show all steps

lock

Thanks for your feedback!

Find the derivative. $$ y=\left(\tan ^{-1} x\right)^{3} $$

Play audio

Feedback

Powered by NumerAI

Audrey Fong and 86 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Derivative of Inverse Trigonometric Functions

Differentiating inverse trigonometric functions involves using specific formulas for their derivatives. In particular, the derivative of arctan(x) is 1/(1 + x^2), and this formula is essential when arctan(x) is nested within other functions.

Power Rule

The power rule is a basic tool in differentiation which applies when a function is raised to a constant exponent. According to the power rule, if a function is in the form of u(x)^n, its derivative is n*u(x)^(n-1) multiplied by the derivative of u(x).

Chain Rule

The chain rule is a fundamental technique in differentiation that is used when dealing with composite functions. It states that to differentiate a composite function, you differentiate the outer function evaluated at the inner function and then multiply by the derivative of the inner function.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later