Taking the derivative of natural log with chain rule

The video tutorial explains the concept of a function inside a function, using implicit differentiation and the chain rule. It introduces the idea of function composition and demonstrates how to derive implicitly by treating a function as a function of another variable. The tutorial provides a step-by-step process for implicit derivation, using U substitution to simplify the function. The video concludes with a recap of the implicit differentiation process and its relation to the chain rule.

What is the inside function in the example discussed in the video?

• X^2 + 1

• ln(X)

• 2X

• X^3 + 1

How can the function be represented for implicit differentiation?

• As 2X

• As ln(U) where U = X^2 + 1

• As X^2 + 1

• As ln(X)

What is the derivative of the inside function X^2 + 1?

• 1

• X^2

• X

• 2X

What is the final derivative of the function using implicit differentiation?

• X^2 / (X^2 + 1)

• 2X / (X^2 + 1)

• 1 / (X^2 + 1)

• 2 / (X^2 + 1)

How does the implicit differentiation result compare with the chain rule?

• It is different

• It is less accurate

• It is the same

• It is more complex