Differentiation of Polynomials and Simple Quotients

The video tutorial covers differentiation, starting with an overview of the concept and the general formula for differentiating functions. It provides three examples: differentiating a polynomial, an expression with brackets, and a quotient. Each example is broken down step-by-step, demonstrating the application of differentiation rules and simplification techniques to find gradients.

What is the result of differentiating the term 3X^3 using the general formula?

• 12X^2

• 3X^2

• 6X^2

• 9X^2

When differentiating a polynomial with brackets, what is the first step?

• Expand the brackets

• Combine like terms

• Simplify the expression

• Differentiate each term directly

What is the derivative of 12X^2 after expanding the brackets?

• 24X

• 48X

• 12X

• 6X

In the quotient example, what is the simplified form of X^2 / X^(1/2)?

• X^(3/2)

• X^(1/2)

• X^2

• X

What is the final simplified form of the expression 3X^2 - 2 / 2X root X?

• 3X^2 - 2 / X^(1/2)

• 3X^2 - 2 / 2X

• 3X^2 - 2 / 2X^(3/2)

• 3X^2 - 2 / X