How to Find Derivatives of Inverse Trigonometric Functions

TL;DR

To find derivatives of inverse trigonometric functions, use specific formulas: the derivative of arcsin(u) is u' / √(1 - u²), arccos(u) is -u' / √(1 - u²), arctan(u) is u' / (1 + u²), and so on. For example, the derivative of arcsin(2x) is 2 / √(1 - 4x²). Each function has a corresponding formula based on the variable u.

Transcript

in this video we're going to go over the derivatives of inverse trig functions so let's start with inverse sine the derivative of the inverse sine function let's say inverse sine of u where u is a function of x the derivative is going to be u prime divided by the square root 1 minus u squared so let's apply this problem or this formula to a particu... Read More

Key Insights

• 🪡 The derivatives of inverse trig functions have specific formulas that need to be applied.
• ❎ The derivative of the inverse sine function is u prime divided by the square root of 1 minus u squared.
• ❎ The derivative of the inverse cosine function is negative u prime divided by the square root of 1 minus u squared.
• ➕ The derivative of the inverse tangent function is u prime divided by 1 plus u squared.
• ❎ The derivative of the inverse secant function is positive u prime divided by the absolute value of u times the square root of u squared minus 1.
• ❎ The derivative of the inverse cotangent function is negative u prime divided by 1 plus u squared.

Questions & Answers

Q: How do you find the derivative of inverse sine?

The derivative of inverse sine of u is u prime divided by the square root of 1 minus u squared.

Q: What is the formula for the derivative of inverse cosine?

The derivative of inverse cosine of u is negative u prime divided by the square root of 1 minus u squared.

Q: How do you find the derivative of inverse tangent?

The derivative of inverse tangent of u is u prime divided by 1 plus u squared.

Q: What is the formula for the derivative of inverse secant?

The derivative of inverse secant of u is positive u prime divided by the absolute value of u times the square root of u squared minus 1.

Summary & Key Takeaways

• The video discusses the derivative of the inverse sine function, which is given by u prime divided by the square root of 1 minus u squared.

• It also covers the derivative of the inverse cosine function, which is negative u prime divided by the square root of 1 minus u squared.

• The derivative of the inverse tangent function is explained as u prime divided by 1 plus u squared.