Derivative of arcsine and simplify to common denominators

The video tutorial explains how to find the derivative of Y prime using the inverse sine formula. It covers the application of the product rule and chain rule, emphasizing the importance of using parentheses to avoid mistakes. The tutorial also demonstrates how to simplify expressions and combine terms to finalize the calculation of Y prime.

What is the formula for the derivative of inverse sine?

• 1 / sqrt(1 - X^2)

• X^2 / (1 - X^2)

• X / sqrt(1 - X^2)

• 1 / (1 + X^2)

Which rule is applied when differentiating a product of two functions?

• Chain Rule

• Product Rule

• Quotient Rule

• Power Rule

What is the purpose of the chain rule in differentiation?

• To differentiate a composite function

• To differentiate a sum of functions

• To differentiate a product of functions

• To differentiate a constant function

Why is it important to use parentheses in mathematical expressions?

• To avoid calculation errors

• To make the expression look neat

• To reduce the number of terms

• To increase the complexity

What happens if you forget to use parentheses in an expression?

• The expression becomes invalid

• The expression remains unchanged

• It can lead to incorrect results

• It simplifies the expression

What is the common denominator used in the final expression for Y prime?

• 1 + X^2

• 1 - X^2

• X^2

• sqrt(1 - X^2)

What is the final expression for Y prime?

• 1 + X^2 / (1 - X^2)

• 2 - 2X^2 / (1 - X^2)

• 2X^2 / (1 - X^2)

• 1 - X^2 / (1 + X^2)