Differentiation and Chain Rule Concepts

The video tutorial reviews the chain rule of differentiation, focusing on differentiating composite functions. It provides two examples: differentiating f(x) = 2 sin(x^3) and g(x) = 2(sin x)^3. The process involves identifying the inner function, calculating its derivative, and applying the chain rule to find the derivative of the composite function. The tutorial emphasizes rewriting the derivative in terms of the original variable.

What is the primary purpose of the chain rule in differentiation?

• To integrate composite functions

• To differentiate composite functions

• To differentiate simple functions

• To find the limit of a function

In the function f(x) = 2 sin(x^3), what is the inner function?

• sin(x^3)

• 2 sin(x)

• 2x^3

• x^3

What is the derivative of the inner function x^3 in the example f(x) = 2 sin(x^3)?

• 3x^2

• 2x^2

• x^2

• 3x

In the function g(x) = 2(sin x)^3, what is the derivative of the inner function sin x?

• 2cos(x)

• cos(x)

• 3sin^2(x)

• sin(x)

What is the final expression for the derivative of g(x) = 2(sin x)^3?

• 6 sin^2(x) * cos(x)

• 6 cos^2(x) * sin(x)

• 2 sin^3(x) * cos(x)

• 3 sin^2(x) * cos(x)