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Derivatives of Inverse Trig

Derivatives of arcsin, arccos, arctan.

Key idea

Derivatives of arcsin, arccos, arctan.

In depth

d/dx arcsin x = 1/√(1 − x²), d/dx arccos x = −1/√(1 − x²), d/dx arctan x = 1/(1 + x²). They come from implicit differentiation of sin y = x and a right triangle.

Worked example

d/dx arctan(2x) = 2/(1 + 4x²).

Formula

(arctan x)′ = 1/(1+x²)

Real-world uses

Common mistake

Mixing arcsin with its reciprocal csc.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Derivatives of Inverse Trig?

Derivatives of arcsin, arccos, arctan. It is a topic at the expert level in Calculus.

What is the formula for Derivatives of Inverse Trig?

The key formula is (arctan x)′ = 1/(1+x²).

Where is Derivatives of Inverse Trig used in real life?

Real-world examples: Integrating in engineering problems involving angles and circular motion.

What should I learn before Derivatives of Inverse Trig?

Make sure you are comfortable with Derivative of ln x, the previous topic in Calculus.

What is a common mistake with Derivatives of Inverse Trig?

Mixing arcsin with its reciprocal csc.

How can I practise Derivatives of Inverse Trig?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Derivatives of Inverse Trig?

Move on to Implicit Differentiation next.

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