Introduction to Differentiation and Applying Differentiation Formulae

The video tutorial covers the concept of differentiation, starting with a review of the original function as the instantaneous rate of change. It explains differentiation from first principles using the formula F'(X) = lim(H→0) [F(X+H) - F(X)]/H. The tutorial explores the application of this formula to functions like 1/X and verifies its correctness for rational values. An example of differentiating 6√X is provided, demonstrating the use of the formula to find derivatives.

What is the formula used to differentiate a function from first principles?

• F'(X) = [F(X + H) - F(X - H)] / 2H

• F'(X) = [F(X + H) + F(X)] / H

• F'(X) = lim (H -> 0) [F(X) - F(X - H)] / H

• F'(X) = lim (H -> 0) [F(X + H) - F(X)] / H

When applying the differentiation formula to 1/X, what is the resulting derivative?

• -1/X^2

• -1/X

• 1/X^2

• 1/X

What is the general conclusion about the differentiation formula for rational values?

• It is not applicable to negative values.

• It only works for positive integers.

• It only works for whole numbers.

• It works for all rational values.

In the example of differentiating 6√X, what is the derivative obtained?

• 3/√X

• 6/√X

• 3X^(-1/2)

• 6X^(-1/2)

What is the value of N when differentiating the function 6√X?

• 1

• 3

• 1/2

• 2