Differentiation Techniques and Rules

The video tutorial covers the application of differentiation rules, focusing on the chain rule, quotient rule, and product rule. It begins with a detailed explanation of the chain rule using the sine function, followed by an example involving the tangent function that combines both chain and quotient rules. The tutorial concludes with the product rule applied to a combination of a polynomial and a cosine function. The instructor emphasizes the importance of practice in mastering these concepts.

What is the derivative of the inside function when differentiating sin(3x)?

• 3x

• x

• 3

• 1

When using the chain rule, what does the derivative of sin(u) become?

• sin(u)

• cos(u)

• tan(u)

• sec(u)

Which rule is used alongside the chain rule to differentiate tan(x/(x-1))?

• Sum rule

• Power rule

• Quotient rule

• Product rule

What is the derivative of the inside function x/(x-1) in the context of tan(x/(x-1))?

• 1

• -1

• x

• x-1

What does the derivative of tan(u) become when using the chain rule?

• cos^2(u)

• tan^2(u)

• sec^2(u)

• sin^2(u)

Why is it important to practice differentiation techniques?

• To memorize formulas

• To understand the theory

• To become familiar and proficient

• To avoid using calculators

What is the first step in applying the product rule to differentiate x^3 * cos(x)?

• Add x^3 and cos(x)

• Multiply x^3 and cos(x)

• Differentiate cos(x)

• Differentiate x^3

What is the derivative of cos(x) when applying the product rule?

• sin(x)

• -cos(x)

• -sin(x)

• cos(x)

In the product rule, what is the derivative of x^3?

• x^3

• 3x^2

• x^2

• 3x

What is the final expression for the derivative of x^3 * cos(x) using the product rule?

• 3x^2 * sin(x) - x^3 * cos(x)

• 3x^2 * cos(x) + x^3 * sin(x)

• 3x^2 * cos(x) - x^3 * sin(x)

• 3x^2 * sin(x) + x^3 * cos(x)