How to take the second derivative using implicit differentiation

The video tutorial explains how to find the second derivative of a function. It begins with finding the first derivative using the chain rule and solving for dy/dx. The tutorial then proceeds to find the second derivative through implicit differentiation, applying the quotient rule. The instructor provides step-by-step guidance and clarifies common questions, emphasizing the beauty and logic of mathematics.

What rule is primarily used to find the first derivative in the given problem?

• Power Rule

• Chain Rule

• Sum Rule

• Quotient Rule

What is the notation used to represent the second derivative?

• dy/dx

• f'(x)

• d²y/dx²

• y'

Which rule is applied to find the second derivative of negative y over x?

• Power Rule

• Quotient Rule

• Product Rule

• Chain Rule

What is the final expression for the second derivative after simplification?

• y squared over x

• x over y

• 2y over x squared

• y over x

Why do the x's divide out in the final expression for the second derivative?

• Because they are in the numerator

• Because they are in the denominator

• Because they cancel each other out

• Because they are equal to zero