Differentiation and Chain Rule Concepts

This video tutorial covers the chain rule of differentiation, focusing on finding derivatives of composite functions involving trigonometric functions. It provides a step-by-step guide on applying the chain rule, with examples including derivatives of functions like H(x) = 3cos(2x^3), G(x) = 9sec(4x+5), and others. Each example demonstrates identifying the inner and outer functions, calculating derivatives, and simplifying results.

What is the chain rule used for in differentiation?

• Finding the derivative of a composite function

• Finding the limit of a function

• Finding the derivative of a single function

• Finding the integral of a function

In the function H(x) = 3 cos(2x^3), what is the inner function?

• 3x^2

• cos(2x^3)

• 2x^3

• 3 cos(x)

What is the derivative of the inner function 2x^3 in the first example?

• 6x^2

• 3x^2

• 2x^2

• 6x

In the function G(x) = 9 sec(4x + 5), what is the derivative of the inner function 4x + 5?

• 5

• 4

• 9

• 1

What is the outer function in the example G(x) = 9 sec(4x + 5)?

• sec(x)

• 9x

• 4x + 5

• tangent(x)

In the function H(x) = 5 cos^3(x), what does the expression 'cos^3(x)' mean?

• cos(x) plus 3

• cos(x) raised to the power of 3

• 3 times cos(x)

• cos(x) divided by 3

What is the derivative of the inner function cos(x) in the third example?

• -cos(x)

• -sin(x)

• cos(x)

• sin(x)

In the function f(x) = 2 csc(2x^5 + 3x), what is the inner function?

• 2x^5

• csc(x)

• 2x^5 + 3x

• 3x

What is the derivative of the inner function 2x^5 + 3x in the final example?

• 10x^4 + 3

• 5x^4 + 3

• 10x^5 + 3

• 2x^4 + 3

What is the outer function in the example f(x) = 2 csc(2x^5 + 3x)?

• 2x^5 + 3x

• 3x

• 2x^5

• csc(x)