How to use the product rule then chain rule with secant

The video tutorial explains how to apply the product rule and chain rule in calculus to find derivatives of complex functions. It begins with an introduction to the product rule, followed by a step-by-step application to specific functions. The tutorial highlights challenges in deriving the secant function and demonstrates the use of the chain rule to address these challenges. Finally, it combines the results to form the final derivative expression.

What is the product rule used for in calculus?

• To integrate a product of two functions

• To differentiate a product of two functions

• To find the limit of a function

• To differentiate a sum of functions

What is the derivative of the function F(x) = 5x^2?

• 10x

• 5x

• 15x

• 20x

Why is the chain rule necessary for differentiating secant(3x)?

• Because secant(3x) is a polynomial

• Because 3x is a constant

• Because secant(3x) is a composite function

• Because secant is a trigonometric function

What is the derivative of G(x) = secant(x) using the chain rule?

• Tangent(x) * Sine(x)

• Secant(x) * Cosine(x)

• Cosine(x) * Tangent(x)

• Secant(x) * Tangent(x)

What is the final expression for the derivative of the product of F(x) = 5x^2 and G(x) = secant(3x)?

• 15x secant(3x) + 10x^2 secant(3x) tangent(3x)

• 10x secant(3x) + 5x^2 secant(3x) tangent(3x)

• 5x secant(3x) + 10x^2 secant(3x) tangent(3x)

• 10x secant(3x) + 15x^2 secant(3x) tangent(3x)