Understanding the Chain Rule in Differentiation

The video tutorial explains how to determine the derivative of a composite function using the chain rule. It begins by identifying the inner and outer functions, then applies the chain rule to find the derivative. The process involves substituting the inner function with 'U', rewriting the function in terms of 'U', and then finding the derivative. The tutorial concludes by simplifying the derivative and expressing it in terms of the original variable.

What is the initial function given in the problem?

• f(x) = x^3 - 4

• f(x) = sqrt(x^3 - 4)

• f(x) = x^2 + 4

• f(x) = sqrt(x^2 - 4)

What type of function is identified in the problem?

• Quadratic function

• Linear function

• Composite function

• Exponential function

What rule is applied to find the derivative of a composite function?

• Power rule

• Chain rule

• Quotient rule

• Product rule

What is the inner function U in this problem?

• U = x^2 - 4

• U = x^3 + 4

• U = x^3 - 4

• U = sqrt(x^3 - 4)

How is the square root function rewritten using a rational exponent?

• U^3

• U^1/2

• U^1/3

• U^2

What is the derivative of U to the 1/2 power?

• 2 U^(1/2)

• 1/2 U^(-1/2)

• 1/2 U^(1/2)

• 2 U^(-1/2)

What is U prime in this problem?

• x^3

• 3x

• 3x^2

• x^2

What is the simplified form of the derivative function?

• 3x^2 / (2 sqrt(x^3 - 4))

• 3x / (2 sqrt(x^3 - 4))

• x^2 / (2 sqrt(x^3 - 4))

• 3x^2 / (sqrt(x^3 - 4))

What is the final form of the denominator in the simplified derivative?

• 2 (x^3 - 4)

• 2 (sqrt(x^3 - 4))

• sqrt(x^3 - 4)

• 2 (x^3 - 4)^2

What is the key takeaway from applying the chain rule?

• It is used for integration.

• It helps in finding the derivative of composite functions.

• It is used for solving linear equations.

• It simplifies the function.