Learn how to take derivative using the quotient rule inside of the chain rule

The video tutorial explains the process of function composition, focusing on identifying inside and outside functions. It covers the application of the chain rule and the quotient rule to find derivatives, emphasizing the importance of simplification. The tutorial guides through calculating the derivative of a composed function, ensuring the correct application of mathematical rules to achieve a simplified final result.

What is the purpose of identifying inside and outside functions in composition?

• To simplify the function

• To determine the domain of the function

• To find the range of the function

• To ensure the inside function results in the original function when plugged into the outside function

Which rule is primarily used to find the derivative of the inside function in this context?

• Sum Rule

• Quotient Rule

• Power Rule

• Product Rule

What is the first step in applying the chain rule to a composition of functions?

• Find the derivative of the inside function

• Find the derivative of the outside function

• Multiply the derivatives of both functions

• Simplify the expression

How is the final expression simplified after applying the chain rule?

• By adding all coefficients

• By dividing the expression by the highest power

• By multiplying the derivatives and simplifying like terms

• By expanding all terms

What is the result of multiplying the derivatives in the chain rule application?

• An expression that needs to be expanded

• A final answer that is further simplified

• A complex expression with multiple variables

• A simplified expression with no fractions