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Introduction to Differentiation and Applying Differentiation Formulae

Introduction to Differentiation and Applying Differentiation Formulae

Assessment

Interactive Video

Mathematics

University

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

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.

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5 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

-1/X^2

-1/X

1/X^2

1/X

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

3/√X

6/√X

3X^(-1/2)

6X^(-1/2)

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

1

3

1/2

2

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